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41.
A body is falling freely under gravity. The distances covered by the body in first, second and third minute of its motion are in the ratio

1 : 4 : 9

1 : 2 : 3

1 : 3 : 5

1 : 5 : 6

1 : 3 : 5

Distance covered in a particular time is

$s_{n} = u + \frac{1}{2} g (2 n - 1) ∴ s_{1} = 0 + \frac{1}{2} g (2 \times 1 - 1) = \frac{g}{2} s_{2} = 0 + \frac{1}{2} g (2 \times 2 - 1) = \frac{3}{2} g and s_{3} = 0 + \frac{1}{2} g (2 \times 3 - 1) = \frac{5}{2} g$

Hence, the required ratio is

$s_{1} : s_{2} : s_{3} = \frac{g}{2} : \frac{3}{2} g : \frac{5}{2} g = 1 : 3 : 5$

42.

A bullet fired into a fixed wooden block loses half of its velocity after penetrating 40 cm. It comes to rest after penetrating a further distance of

$\frac{22}{3} cm$
$\frac{40}{3} cm$
$\frac{20}{3} cm$
$\frac{22}{5} cm$

43.

A ball A is thrown up vertically with a speed u and at the same instant another ball B is released from a height h. At time t, the speed of A relative to B is

u
2u
u − gt
$\sqrt{(u^{2} - gt)}$

44.

A bullet is to be fired with a speed of 2000 ms^-1 to hit a target 200 m away on a level ground. If g = 10 ms^-2, the gun should be aimed

directly at the target
5 cm below the target
5 cm above the target
2 cm above the target

45.

A particle starts from rest at t = 0 and moves in a straight line with an acceleration as shown in figure. The velocity of the particle at t = 3 s is

2 ms^-1
4 ms^-1
6 ms^-1
8 ms^-1

46.

Two cars A and B are moving with same speed of 45 km/h along same direction. If a third car C coming from the opposite direction with a speed of 36 km/h meets two cars in an interval of 5 min, the distance of separation of two cars A and B should be (in km)

6.75
7.25
5.55
8.35

47.

Two trains are moving with equal speed in opposite directions along two parallel railway tracks. If the wind is blowing with speed u along the track so that the relative velocities of the trains with respect to the wind are in the ratio 1 : 2, then the speed of each train must be

48.

Two balls are dropped to the ground from different heights. One ball is dropped 2 s after the other but they both strike the ground at the same time. If the first ball takes 5 s to reach the ground, then the difference in initial heights is (g = 10 ms^-2)

20 m
80 m
170 m
40 m

49.

A ball is thrown vertically upwards with a velocity of 25 ms^-1 from the top of a tower of height 30 m. How long will it travel before it hits ground ?