Question

A potato cannon fires a potato so that it has initial velocity with components of (60 m/s forward, 50 m/s upward).(a) How much time passes before the potato strikes the ground?______ s(b) What horizontal distance does the potato travel before striking the ground?______ m

Answer 1

The vertical motion of a projectile can be described using the equations for uniformly accelerated motion, while the horizontal motion is described by the equations for uniform rectilinear motion.

The time that it takes for an object to reach the ground once it is thrown vertically with a speed v is given by:

`t=(2v_0)/(g)`

Where g is the acceleration of gravity:

`g=9.8(m)/(s^2)`

Substitute the value of g and v₀=50m/s (the upward velocity) to find the time that it takes for the potato to strike the ground:

`t=(2(50(m)/(s)))/(9.8(m)/(s^2))=10.2s`

During that time, the potato is also moving horizontally with a constant speed of 60m/s. The distance d traveled by an object with constant speed v in a time t is:

`d=vt`

Substitute v=60m/s and t=10.2s to find the horizontal distance that the potato travels before striking the ground:

`\begin{gathered} d=(60(m)/(s))(10.2s) \\ =612m \end{gathered}`

Therefore, the answers are:

`\begin{gathered} a) \\ 10.2s \end{gathered}`
`\begin{gathered} b) \\ 612m \end{gathered}`