Motion in A Straight Line Test

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Motion in A Straight Line Test - 46

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Question 1
1 / -0

A man can swim with a speed of 4 $$km h^{-1}$$ in still water. He crosses a river 1 km wide that flows steadily at 3 $$kmh^{-1}$$. If he makes his strokes normal to the river current, how far down the river does he go when he reaches the other bank?

A
500 m

B
600 m

C
750 m

D
850 m

Solution

Time to cross the river, $$t=\dfrac{Width \ of \ river}{Speed \ of \ man}+\dfrac{1km}{4 kmh^{-1}}$$
$$=\dfrac{1}{4}h$$
Distance moved along the river in time t,
$$s= v_{r} \times t = 3kmh^{-1}\times \dfrac{1}{4}h $$
$$= \dfrac{3}{4}km = 750m$$
Question 2
1 / -0

A rocket of initial mass $$6000\ kg$$ eject gases at a constant rate of $$16\ kg s^{-1}$$ with constant relative speed of $$11\ kms^{-1}$$. What is the acceleration of rocket one minute after the blast?

A
$$25 ms^{-2}$$

B
$$50 ms^{-2}$$

C
$$10 ms^{-2}$$

D
$$35 ms^{-2}$$

Solution

Acceleration of the rocket at any instant t is
$$a = \dfrac{v_r\dfrac{dm}{dt}}{M-t\dfrac{dm}{dt}}$$
Here, M=6000 kg, $$\dfrac{dm}{dt}=16 kg s^{-1}$$
$$v_r=11 km^{-1}= 11000 ms^{-1}$$, t=1 min = 60 s
$$\therefore a=[\dfrac{11000\times 16}{6000-60\times 16}]ms^{-2}=35 ms^{-2}$$
Question 3
1 / -0

A car travels with a uniform velocity of $$20\,\,m{s^{ - 1}}$$ for 5 sec. The brakes are then applied and the car is uniformly retarded. It comes to rest in further 8 sec by drawing a graph between velocity and time-find.

A
The distance traveled in the first 5 sec.

B
The distance traveled after the brakes are applied.

C
Total distance traveled.

D
Acceleration during the first 5 sec.

E
Acceleration during the last 8 sec.

Solution
Question 4
1 / -0

A ball rolls off the top of a stairway horizontally with a velocity of $${ 4.5\ ms }^{ -1 }$$. Each steps is $$0.2\ m$$ high and $$0.3\ m$$ wide. If $$g$$ is $${ 10\ ms }^{ -2 }$$, and the ball strikes the edge of the $$nth$$ step, then $$n$$ is equal to:

A
$$9$$

B
$$10$$

C
$$11$$

D
$$12$$

Solution

It strikes on $${ n }^{ th }$$ step edge.
Therefore, $$4.5t=0.3n$$

$$\Rightarrow \quad t=\dfrac { n }{ 15 } $$

$$\dfrac { 1 }{ 2 } { gt }^{ 2 }=0.2n$$

$$\dfrac { 1 }{ 2 } \times 10\times \dfrac { { n }^{ 2 } }{ { 15 }^{ 2 } } =0.2n$$

$$\Rightarrow \quad n=9$$
Question 5
1 / -0

A body is dropped from a balloon moving up with a velocity of $$4\ m/s$$ when the balloon is at a height of $$120.5\ m$$ from the ground. The height of the body after $$5\ s$$ from the ground is? $$(g = 9.8\ ms^{-2})$$.

A
$$8\ m$$

B
$$12\ m$$

C
$$18\ m$$

D
$$24\ m$$

Solution

Given,
$$u=4m/s$$
$$g=9.8m/s^2$$
$$t=5sec$$
$$H=120.5m$$
From 2nd equation of motion,
$$-S=ut-\dfrac{1}{2}gt^2$$
$$-S=4\times 5-\dfrac{1}{2}\times 9.8\times 5\times 5$$
$$S=-20+122.5=102.5m$$
Height of the body after 5 sec,
$$h=H-S$$
$$h=120.5-102.5$$
$$h=18m$$
The correct option is C.
Question 6
1 / -0

The displacement of a body at any time $$t$$ after starting is given by $$s = 15t - 0.4 t^{2}$$. Find the time when the velocity of the body will be $$7\ ms^{-1}$$.

A
$$ t=20\,s$$

B
$$t=10\,s$$

C
$$ t=30\,s$$

D
$$ t=40\,s$$

Solution

$$S=15t-0.4t^{2}$$

$$\dfrac{ds}{dt}=15-0.8t$$

$$\vartheta =\dfrac{ds}{dt}$$ so,

$$\vartheta =15-0.8t$$

Given, $$\vartheta =7$$

$$7=15-0.8t$$

$$t=10$$ sec
Question 7
1 / -0

A balloon is ascending vertically with an acceleration of 1 $$ms^{-2}$$. Two stones are dropped from it at an interval of 2 s. Find the distance between them 1.5 s after the second stone is released.

A
35 m

B
45 m

C
55 m

D
None of these

Solution

(This method can be understood in a proper way after studying relative velocity.)
If we work from the frame of the balloon, then the acceleration of each stone w.r.t. the balloon will be g + a after releasing from it. The initial velocity of each stone will be zero w.r.t. balloon.
$$S_1 = 1/2 (g + a)(3.5)^2$$, $$S_2 = (1/2)(g + a)(1.5)^2; x = S_1 - S_2$$ = 55m
Question 8
1 / -0

A car starting from rest accelerates at the rate $$f$$ through a distance $$S$$, then continues at constant speed for time $$t$$ and then decelerates at the rate $$f/2$$ to come to rest. If the total distance traversed is $$5\ S$$, then

A
$$S = ft$$

B
$$S = 1/6\ ft^{2}$$

C
$$S = 1/2\ ft^{2}$$

D
$$S = 1/4\ ft^{2}$$

Solution

$$s_{1} + s_{2} + s_{3} = 5s$$
$$\Rightarrow s + vt + \dfrac {v^{2}}{f} = 5s$$
$$\Rightarrow 4s = vt + \dfrac {v^{2}}{f} = \sqrt {2fs}\times t + \dfrac {2fs}{f}$$
$$\Rightarrow 2s = t\sqrt {2fs} \Rightarrow s = \dfrac {1}{2}ft^{2}$$.
Question 9
1 / -0

A ball of mass $$0.2kg$$ is thrown vertically upwards by applying a force by hand. If the hand moves $$0.2m$$ which applying the force and the ball goes upto $$2m$$ height further, find the magnitude of the force. Consider $$g=10m/{s}^{2}$$

A
$$22N$$

B
$$4N$$

C
$$16N$$

D
$$20N$$

Solution

(i) $${ v }^{ 2 }={ u }^{ 2 }+2ay$$
$$0={ v }^{ 2 }-2(g)2$$
(ii) $${ v }^{ 2 }=0+2a(0.2)$$
$$a=100$$
(iii) $$F=ma=0.2\times 100=20N$$
Question 10
1 / -0

A parachutist after bailing out falls $$50\ m$$ without friction. When parachute opens, it decelerates at $$2\ m/s^{2}$$. He reaches the ground with a speed of $$3\ m/s$$. At what height, did he bail out?

A
$$91\ m$$

B
$$182\ m$$

C
$$293\ m$$

D
$$111\ m$$

Solution

$$A\rightarrow B$$
$$v^{2} = u^{2} + 2as$$
$$v^{2} = 0 +2\times 9.8\times 50$$
$$v = \sqrt {980} m/s$$
From $$B\rightarrow C$$
$$V^{2} = u^{2} + 2as$$
$$(3)^{2} = 980 - 2\times 2\times s$$
$$s = 242.75$$
Total height $$= 242.72 + 50 =292.75\approx 293\ m$$.

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Motion in A Straight Line Test - 46

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Motion in A Straight Line Test - 46

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SHARING IS CARING

Question 1

500 m

600 m

750 m

850 m

Solution

Question 2

$$25 ms^{-2}$$

$$50 ms^{-2}$$

$$10 ms^{-2}$$

$$35 ms^{-2}$$

Solution

Question 3

The distance traveled in the first 5 sec.

The distance traveled after the brakes are applied.

Total distance traveled.

Acceleration during the first 5 sec.

Acceleration during the last 8 sec.

Solution

Question 4

$$9$$

$$10$$

$$11$$

$$12$$

Solution

Question 5

$$8\ m$$

$$12\ m$$

$$18\ m$$

$$24\ m$$

Solution

Question 6

$$ t=20\,s$$

$$t=10\,s$$

$$ t=30\,s$$

$$ t=40\,s$$

Solution

Question 7

35 m

45 m

55 m

None of these

Solution

Question 8

$$S = ft$$

$$S = 1/6\ ft^{2}$$

$$S = 1/2\ ft^{2}$$

$$S = 1/4\ ft^{2}$$

Solution

Question 9

$$22N$$

$$4N$$

$$16N$$

$$20N$$

Solution

Question 10

$$91\ m$$

$$182\ m$$

$$293\ m$$

$$111\ m$$

Solution

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