A 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?
We know that the maximum range Rmax and maximum height hmax are given by
If the ball is thrown vertically upwards, and Eq. (ii) reduces to
Comparing (i) and (ii) we get
The maximum height attained by a projectile and its horizontal range are equal to each other if the projectile is projected at an angle θ given by
When a projectile is at the highest point of its trajectory, the directions of its velocity and acceleration are
A 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?
A 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
A 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.
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)
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
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
The speed of projection of projectile is increased by 5%, without changing the angle of projection. The percentage increase in the range will be
A projectile has the same range R when the maximum height attained by it is either h1 or h2. Then R, h1 and h2 will be related as