Question

A cannonball is fired horizontally with an initial velocity of 20 m/s off a cliff that is 10 m from the ground. if the initial velocity is doubled what will be the affect on the time and horizontal distance?

A) Both the time and horizontal distance will double.
B) Neither the time or horizontal distance will change.
C) The time won't change, but horizontal distance will double.
D) The time will double, but the horizontal distance won't change.

Answer 1

C) The time won't change, but horizontal distance will double.

Step-by-step explanation:

The time won't change, but horizontal distance will double. The time is based on the acceleration due to gravity (g) and the vertical distance, so it will not change. If the horizontal velocity changes, the horizontal distance will double based on the formula d=tv.

Answer 2

Consider the motion of the cannonball along the vertical direction or y-direction.

`v_(oy)` = initial velocity along the Y-direction

`a_(y)` = acceleration due to gravity

t = time of travel

Y = vertical displacement

Using the kinematics equation

Y =
`v_(oy)` t + (0.5)
`a_(y)` t²

since the ball has been launched horizontally ,
`v_(oy)` = 0

Y = (0) t + (0.5)
`a_(y)` t²

t =
`(2Y)/(a_(y))`

hence the time of travel is independent of the initial velocity. hence the time of travel remain same.

Consider the motion along the horizontal direction

`v_(ox)` = initial velocity along the X-direction

`a_(x)` = acceleration along the horizontal direction = 0

t = time of travel

X = horizontal displacement

Using the kinematics equation

X =
`v_(ox)` t + (0.5)
`a_(x)` t²

since the ball has been launched horizontally ,
`a_(x)` = 0

X =
`v_(ox)` t + (0.5) (0) t²

X =
`v_(ox)` t

hence the horizontal distance directly depends on the velocity. so the horizontal distance will become double.

C) The time won't change, but horizontal distance will double.