Question

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?

Answer 1

2.85 s .

Step-by-step 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 .

Answer 2

2.85 s .

Step-by-step 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 .