Question

A projectile launched at 45° with a velocity of 100m/s hits a target what will be the velocity if the range is doubled?

Answer 1

Answer:

If the range of the projectile is doubled then the velocity will be 141.4 m/s.

Explanation:

The velocity with which the projectile is thrown, u = 100 m/s

The angle made by the projectile, θ = 45°

This is the condition for the projectile to cover a maximum distance. The equation for the maximum range is:

R (max) = u²/g

Where g is the acceleration due to gravity acting on the projectile.

∴ R (max) = 100² / 9.8

  R (max) = 1020.4 m

If the range is doubled, R' = 2R

                                       R' = 2 × 1020.4

                                       R' = 2040.8 m

Now the velocity required to cover this distance can be calculated as:

u² = R' × g

u² = 2040.8 × 9.8

u² = 19999.84

u = √19999.84

u = 141.4 m/s