51. A ball is thrown vertically downward with a velocity of 20 m/s from the top of a tower. It hits the ground after some time with a velocity of 80 m/s. The height of the tower is: (g = 10 m/s2)

50. A stone falls freely under gravity. It covers distances h1, h2 and h3 in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively: The relation between h1, h2 and h3 is

49. A boy standing at the top of a tower of 20 m height drops a stone. Assuming g = 10 ms−2 , the velocity with which it hits the ground is

49. A boy standing at the top of a tower of 20 m height drops a stone. Assuming g = 10 \(ms^{−2}\)  , the velocity with which it hits the ground is

(a) 10.0 m/s

(b) 20.0 m/s

(c) 40.0 m/s

(d) 5.0 m/s

Answer :  (b) 20.0 m/s

\( v^2 = u^2 + 2as \)

\( = 0 + 2(10)(20) \)

\(= 400 \)

\( v = \sqrt{400} = 20\) m/s 

48. A ball is dropped from a high rise platform at t = 0 starting from rest. After 6 seconds another ball is thrown downwards from the same platform with a speed v. The two balls meet at t = 18 s. What is the value of v ? ( take g = 10 m/s2 )

47. A man of 50 kg mass is standing in a gravity free space at a height of 10 m above the floor. He throws a stone of 0.5 kg mass downwards with a speed 2 m/s. When the stone reaches the floor, the distance of the man above the floor will be:

46. Two bodies, A (of mass 1 kg ) and B (of mass 3 kg ), are dropped from heights of 16 m and 25 m, respectively. The ratio of the time taken by them to reach the ground is

45. A ball is thrown vertically upward. It has a speed of 10 m/sec when it has reached one half of its maximum height. How high does the ball rise? Take g = 10 m/s2.

44. If a ball is thrown vertically upwards with speed u, the distance covered during the last t seconds of its ascent is

43. A man throws balls with the same speed vertically upwards one after the other at an interval of 2 seconds. What should be the speed of the throw so that more than two balls are in the sky at any time? [ Given g = 9.8 m/s2 ]

42. If a ball is thrown vertically upwards with a velocity of 40 m/s, then velocity of the ball after two seconds will be ( g = 10 m/s2 )

41. A body is thrown vertically upward from the ground. It reaches a maximum height of 20 m in 5 sec. After what time, it will reach the ground from its maximum height position?

40. A stone released with zero velocity from the top of a tower, reaches the ground in 4sec. The height of the tower is ( g = 10 m/s2 )

39. Three different objects of masses m1, m2 and m3 are allowed to fall from rest and from the same point O along three different frictionless paths. The speeds of the three objects on reaching the ground will be in the ratio of

38. The water drops fall at regular intervals from a tap 5 m above the ground. The third drop is leaving the tap at an instant when the first drop touches the ground. How far above the ground is the second drop at that instant? ( Take g = 10 m/s2 )

37. A body dropped from top of a tower fall through 40 m during the last two seconds of its fall. The height of tower is (g = 10 m/s2)

37. A body dropped from top of a tower fall through 40 m during the last two seconds of its fall. The height of tower is (\(g = 10 m/s^2\))

(a) 60 m

(b) 45 m

(c) 80 m

(d) 50 m

Answer :  (b) 45 m

\( s = ut + \)\(\frac{1}{2}\)\(at^2 \)

\( 40 = u_2(2) + \)\(\frac{1}{2}\)\((10)(2)^2 \)

\( 40 = 2u_2 + 20 \)

\(\rightarrow u_2 = 10 \, m/s \)

\( v^2 = u^2 + 2as \)

\( 10^2 = 0 + 2(10)h \)

\( h = 5 \, m \)

total height of the tower = 40 + 5 = 45 m

36. What will be the ratio of the distances moved by a freely falling body from rest in 4th and 5th seconds of journey?