How much force is required to launch a 1 kg pumpkin 10 meters away from 5 meters off the
ground at a launch angle of zero degrees if it takes the catapult 0.1 seconds to fully launch the
pumpkin?

F= 99 N

Explanation:

Dynamics and Kinematics

This problem is a combination of dynamics and kinematics because we need formulas and concepts of both branches of physics to solve it.

We need to calculate the force required to launch horizontally a pumpkin of m=1 Kg a distance of d=10 m away from a height of h=5 m.

Since the force is:

F = m.a

We need to calculate the acceleration required to move the pumpkin from rest (vo=0) to the launching speed (vf) in a time t=0.1 seconds.

The acceleration can be calculated by using the kinematic equation:

The final launching speed vf can be calculated knowing the height and maximum horizontal distance reached by the pumpkin.

When an object is thrown horizontally with a speed vf from a height h, the range or maximum horizontal distance traveled by the object can be calculated as follows:

Solving for vf:

Substituting:

Calculating:

Now we calculate the acceleration:

Thus, the force required is:

F= 99 N

resonant frequency