An NCC parade is going at a uniform speed of

Question: An NCC parade is going at a uniform speed of $6 \mathrm{~km} / \mathrm{h}$ through a place under a berry tree on which a bird is sitting at a height of $12.1 \mathrm{~m}$. A particular instant the bird drops a berry. Which cadet (give the distance from the tree at the instant) will receive the berry on his uniform? Solution: For berry, $u=0 ; a=g ; s=12.1 m$ $\mathrm{s}=\mathrm{ut+}{ }^{\frac{1}{2}} a \mathrm{t}^{2}$ $12.1=0+\frac{1}{2}(g) t^{2}$ $\mathrm{t}=1.57 \mathrm{sec}$ Distance...

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Solve this following

Question: If $A(-2,0), B(0,4)$ and $C(0, k)$ be three points such that area of a $A B C$ is 4 sq units, find the value of $k$. Solution:...

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A healthy young man standing at a distance of

Question: A healthy young man standing at a distance of $7 \mathrm{~m}$ from a $11: 8 \mathrm{~m}$ high building sees a kid slipping from the top floor. With what speed (assumed uniform) should he run to catch the kid at the arms height $(1.8 \mathrm{~m})$ ? Solution: For kid, $\mathrm{u}=0 ; \mathrm{a}=\mathrm{g} ; \mathrm{s}=11.8-1.8$ $\mathrm{s}=10 \mathrm{~m}$ $s=u t+\frac{1}{2} a t^{2}$ $10=0+\frac{1}{2}(g) t^{2}$ $t=1.42 \mathrm{sec}$ In this time, man has to reach building Speed= $\frac{\...

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Solve this following

Question: Find the value of $k$ for which the area of aABC having vertices $A(2,-6), B(5,4)$ and $C(k, 4)$ is 35 sq units. Solution:...

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A person sitting on top of a tall building is dropping balls

Question: A person sitting on top of a tall building is dropping balls at regular intervals of one second. Find the positions of the $3^{\text {rd }}, 4^{\text {th }}$ and $5^{\text {th }}$ ball when the $6^{\text {th }}$ ball is being dropped. Solution: For every ball; $u=0$ and $a=g$ When $6^{\text {th }}$ ball is dropped, $5^{\text {th }}$ ball moves for 1 second, $4^{\text {th }}$ ball moves for 2 seconds, $3^{\text {rd }}$ ball moves for 3 seconds Position $S=u t+{ }^{\frac{1}{2}} a t^{2}$ ...

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Solve this following

Question: Find the value of $k$ for which thepoints $A(1,-1), B(2, k)$ and $C(4,5)$ are collinear. Solution:...

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A stone is thrown vertically upward with a speed of

Question: A stone is thrown vertically upward with a speed of $28 \mathrm{~m} / \mathrm{s}$. (a) Find the maximum height reached by the stone. (b) Find its velocity one second before it reaches the maximum height. (c) Does the answer pf part (b) change if the initial speed is more than $28 \mathrm{~m} / \mathrm{s}$ such as $40 \mathrm{~m} / \mathrm{s}$ or 80 $\mathrm{m} / \mathrm{s}$ ? Solution: (a) $u=28 \mathrm{~m} / \mathrm{s} ; \mathrm{v}=0 \mathrm{~m} / \mathrm{s} ; \mathrm{a}=-\mathrm{g}$ ...

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Find the value of

Question: Find the value of $k$ for which thepoints $P(5,5), Q(k, 1)$ and $R(11,7)$ are collinear. Solution:...

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Solve this following

Question: Find the value of $k$ for which thepoints $A(3,-2), B(k, 2)$ and $C(8,8)$ are collinear. Solution:...

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A ball is dropped from a balloon going up at a speed

Question: A ball is dropped from a balloon going up at a speed of $7 \mathrm{~m} / \mathrm{s}$. if the balloon was at a height $60 \mathrm{~m}$ at the time of dropping the ball, how long will the ball take in reaching the ground? Solution: $\mathrm{u}=7 \mathrm{~m} / \mathrm{s} ; \mathrm{a}=-\mathrm{g} ; \mathrm{s}=-60$ $\mathrm{s}=u t^{\frac{1}{2}} a t^{2}$ $-60=7 t^{\frac{1}{2}}(g) t^{2}$ $\mathrm{t}=4.28 \mathrm{sec}$...

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Use determinants to show that the following points are collinear.

Question: Use determinants to show that the following points are collinear. $P(-2,5), Q(-6,-7)$ and $R(-5,-4)$ Solution:...

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A ball is projected vertically upward with a speed of

Question: A ball is projected vertically upward with a speed of $50 \mathrm{~m} / \mathrm{s}$ Find (a) The maximum height (b) The time to reach the maximum height (c) The specd at half the maximum height. Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$ Solution: $\mathrm{u}=50 \mathrm{~m} / \mathrm{s} ; \mathrm{v}=0 \mathrm{~m} / \mathrm{s} ; \mathrm{a}=-\mathrm{g}$ (a) $\mathrm{v}^{2}=\mathrm{u}^{2}+2 \mathrm{as}$ $0^{2}=(50)^{2}+2(\mathrm{~g}) \mathrm{s}$ $s=125 m$ (b) $v=u+a t$ $0=50$-gt $\...

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Use determinants to show that the following points are collinear.

Question: Use determinants to show that the following points are collinear. $A(3,8), B(-4,2)$ and $C(10,14)$ Solution:...

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A car travelling at

Question: A car travelling at $60 \mathrm{~km} / \mathrm{h}$ overtakes another car travelling at $42 \mathrm{~km} / \mathrm{h}$. Assuming each car to be $5.0 \mathrm{~m}$ long, find the time taken during the overtake and the total road distance used for the overtake. Solution: $\overrightarrow{\mathrm{V}}_{1}=60 \times \frac{5}{18}=16.6 \mathrm{~m} / \mathrm{s}$ $\overrightarrow{\mathrm{V}}_{2}=42 \times \frac{5}{18}=11.6 \mathrm{~m} / \mathrm{s}$ Relative velocity $=16.6-11.6$ $\mathrm{V}_{\tex...

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Use determinants to show that the following points are collinear.

Question: Use determinants to show that the following points are collinear. $A(2,3), B(-1,-2)$ and $C(5,8)$ Solution:...

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A police jeep is chasing a culprit going on a motorbike.

Question: A police jeep is chasing a culprit going on a motorbike. The motorbike crosses a turning at a speed of $72 \mathrm{~km} / \mathrm{h}$. The jeep follows it at a speed of $90 \mathrm{~km} / \mathrm{h}$, crossing the turning ten seconds later than the bike. Assuming that they travel at constant speeds, how far from the turning will the jeep catch up with the bike? Solution: $V_{\text {bike }}=72^{\times \frac{5}{18}}=20 \mathrm{~m} / \mathrm{s}$ $V_{\text {police }}=90^{\times \frac{5}{18...

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Find the area of the triangle whose vertices are:

Question: Find the area of the triangle whose vertices are: $P(1,1), Q(2,7)$ and $R(10,8)$ Solution:...

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Find the area of the triangle whose vertices are:

Question: Find the area of the triangle whose vertices are: $P(0,0), Q(6,0)$ and $R(4,3)$ Solution:...

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Complete the following table:

Question: Complete the following table: Solution: If initial velocity is $\mathrm{u}$ and deacceleration is $-\mathrm{a}$ then braking distance $v^{2}=u^{2}+2 a s$ $0^{2}=u^{2}-2 a S$ $\mathrm{S}_{\mathrm{b}}=\frac{\mathrm{u} 2}{2 \mathrm{a}}$ (Braking distance) $\mathrm{S}_{\mathrm{R}}=\mathrm{u} \times \mathrm{t}_{\mathrm{R}}$ (Reaction distance) Total distance $=\mathrm{S}_{\mathrm{b}}+\mathrm{S}_{\mathrm{R}}$ Solve table with given values and above formulas...

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Find the area of the triangle whose vertices are:

Question: Find the area of the triangle whose vertices are: $A(-8,-2), B(-4,-6)$ and $C(-1,5)$ Solution:...

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A driver takes 0.20 s to apply the brakes after he sees a need for it,

Question: A driver takes $0.20$ s to apply the brakes after he sees a need for it, This is called the reaction time of the driver. If he is driving a car at a speed of $54 \mathrm{~km} / \mathrm{h}$ and the brakes cause a deceleration of $6.0 \mathrm{~m} / \mathrm{s}^{2}$, find the distance travelled by the car after he sees the need to put the brakes on. Solution: Speed of car $=54 \times \frac{5}{18}=15 \mathrm{~m} / \mathrm{s}$ Distance travelled during reaction time $\mathrm{S}_{1}=\mathrm{v...

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Find the area of the triangle whose vertices are:

Question: Find the area of the triangle whose vertices are: $A(-2,4), B(2,-6)$ and $C(5,4)$ Solution:...

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A particle starting from rest moves with constant acceleration.

Question: A particle starting from rest moves with constant acceleration. If it takes $5.0$ s to reach the speed $18.0$ $\mathrm{km} / \mathrm{h}$ Find (a) The average velocity during this period (b) The distance travelled by the particle during this period. Solution: $\mathrm{u}=0 ; \mathrm{t}=5 \mathrm{sec} ; \mathrm{v}=18 \times 5 / 18=5 \mathrm{~m} / \mathrm{s}$ $\mathrm{v}=\mathrm{u}+\mathrm{at}$ $5=0+a(5)$ $a=1 \mathrm{~m} / \mathrm{s}^{2}$ $S=u t^{\frac{1}{2}} a t^{2}$ $\mathrm{S}=0+\frac...

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Find the area of the triangle whose vertices are:

Question: Find the area of the triangle whose vertices are: $A(3,8), B(-4,2)$ and $C(5,-1)$ Solution:...

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A bullet going with speed

Question: A bullet going with speed $350 \mathrm{~m} / \mathrm{s}$ enters a concrete wall and penetrates a distance $5.0 \mathrm{~cm}$ before coming to rest. Find the deceleration. Solution: $\mathrm{u}=350 \mathrm{~m} / \mathrm{s} ; \mathrm{v}=0 ; \mathrm{s}=5 \times 10^{-2} \mathrm{~m}$ $\mathrm{v}^{2}=2^{2}+2 \mathrm{as}$ $0^{2}=(350)^{2}+2(\mathrm{a})(0.05)$ $\mathrm{a}=-12.25 \times 10^{5} \mathrm{~m} / \mathrm{s}^{2}$...

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