Question

From the top of a tower of a height 40 m, a ball is projected upwards with a speed of 20 m/s at an angle of elevation of 30°. The ratio of the total time taken by the ball to hit the ground to its time of flight (time taken to come back to the same elevation) is (Take g = 10 m/s2)

Solution

Correct option is

2 : 1

 

The time of flight  The initial downward velocity = 20 sin 30° = 10 ms-1. The time taken to fall through a height of 40 m with velocity 10 ms-1 is given by

               

or              t2 + 2t – 8 = 0

 which gives t = 2s. Hence the total time to hit the ground

                       = tf + t = 2 + 2 = 4s

SIMILAR QUESTIONS

Q1

ball is projected horizontal with a velocity of 5 ms-1 from the top of a building 19.6 m high. How long will the ball take to hit the ground?

Q2

bomb is dropped from an aero plane when it is at a height h directly above a target. If the aero plane is moving horizontally at a speed v, the distance by which the bomb will miss the target is given by

Q3

missile is fired for maximum range at your town from a place in the enemy country 100 km away from your town. If the missile is first detected at its half – way point, how much warning time will you have? Take g = 10 ms-2.

Q4

cricketer can throw a ball to a maximum horizontal distance of 100 m. With the same effort, he throws the ball vertically upwards. What is the maximum height attained by the ball?

Q5

The maximum height attained by a projectile is increased by 10% by increasing its speed of projection, without changing the angle of projection. The percentage increase in the horizontal range will be

Q6

The maximum height attained by a projectile is increased by 10% by changing the angle of projection, without changing the speed of projection. The percentage increase in the time of flight will be

Q7

The speed of projection of projectile is increased by 5%, without changing the angle of projection. The percentage increase in the range will be

Q8

A projectile has the same range R when the maximum height attained by it is either h1 or h2. Then Rh1 and h2 will be related as

Q9

A relief aeroplane is flying at a constant height of 1960 m with speed 600km/hr above the ground towards a point directly over a person struggling in flood water (see fig.). At what angle if sight, should the pilot release a survival kit if it is to reach the person is water? (g = 9.8 m/s2

                                               

Q10

At a harbour enemy ship is at a distance  from the security cannon having a muzzle velocity of 60 m/s (a) To what angle must the cannon be elevated to hit the ship? (b) What is the time of flight? (c) How far should the ship be moved away from its initial position so that it becomes beyond the range of the cannon? (g = 10 m/s2)