## Question

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

### Solution

10%

We know that The increase *δ* *h* in *h* when *v*_{0} changes by *δ v*_{0}can be obtained by partially differenting this expression. This

Since *h* is increased by 10 %,

Therefore,

Thus *δR* = 0.1 *R.* Hence *R *also increased by 10%.

#### SIMILAR QUESTIONS

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}.

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?

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/s^{2})

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 *h*_{1} or *h*_{2}. Then *R*, *h*_{1} and *h*_{2} will be related as

A relief aeroplane is flying at a constant height of 1960 *m* with speed 600*km/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/s^{2})

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/s^{2})

During volcanic eruption chunks of solid rock are blasted out of the volcano. (a) At what initial speed would a volcanic object have to be ejected at 37° to the horizontal from the vent *A* in order to fall at *B* as shown in fig. (b) What is the time of flight? (g = 9.8 m/s^{2})