First, you will investigate purely vertical motion. The kinematics equation for vertical motion (ignoring air resistance) is given byy (t) = y0+v0t - (1/2) gt2, where y0=0 is the initial position, v0 is the initial speed, and g is the acceleration due to gravity. Drag the cannon downwards so it is at ground level, or 0 m (which represents the initial height of the object), then fire the pumpkin straight upward (at an angle of 90∘) with an initial speed of 14 m/s. How long does it take for the pumpkin to hit the ground?

2.85 s.

Explanation:

y (t) = y (0) + v₀t + 1/2 gt²

y (t) is vertical displacement, y (0) is initial position, v₀ is initial velocity and t is time required to make vertical displacement and g is acceleration due to gravity.

Here y (0) is zero, v₀ = 14 m/s, g = 9.8 m s⁻², y (t) = 0, as the pumpkin after time t comes back to its initial position, that is ground.

We shall take v₀ as negative as it is in upward direction and g as positive as it acts in downward direction

Put the values in the equation above,

0 = 0 - 14t + 1/2 x 9.8 t²

14 t = 1/2 x 9.8 t²

t = 28 / 9.8

t = 2.85 s.

2.85 s.

Explanation:

y (t) = y (0) + v₀t + 1/2 gt²

y (t) is vertical displacement, y (0) is initial position, v₀ is initial velocity and t is time required to make vertical displacement and g is acceleration due to gravity.

Here y (0) is zero, v₀ = 14 m/s, g = 9.8 m s⁻², y (t) = 0, as the pumpkin after time t comes back to its initial position, that is ground.

We shall take v₀ as negative as it is in upward direction and g as positive as it acts in downward direction

Put the values in the equation above,

0 = 0 - 14t + 1/2 x 9.8 t²

14 t = 1/2 x 9.8 t²

t = 28 / 9.8

t = 2.85 s.