A projectile is shot vertically upward with a given initial velocity.It reaches a maximum height of 100 m.If on a second shot the initial velocity is doubled, then the projectile will reach a maximum height of:
A)70.7 m
B)141.4 m
C)200 m
D)241 m
E)400 m

Question

Quizplus · Accepted Answer

The maximum height $h$ reached by a projectile shot vertically upward with initial velocity $v$ is directly proportional to the square of the initial velocity ($v^2$) when air resistance is negligible. Given that the initial shot reaches 100 m, when the initial velocity is doubled, the maximum height will be $4$ times the original height (since $(2v)^2 = 4v^2$). Therefore, the new height will be $4 \times 100\,m = 400\,m$.

A Projectile Is Shot Vertically Upward with a Given Initial