Question

at what rate is the gravitational force on a 9 kg projectile doing work at an instant when the velocity of the projectile is 3.1 m/s directed 34 degrees above the horizontal? hint: it helps to draw a diagram.

Answer 1

The gravitational force is doing work on a 9 kg projectile with velocity 3.1 m/s at a rate of approximately 153.01 watts when the projectile's velocity is directed 34 degrees above the horizontal.

Step-by-step explanation:

To calculate the rate at which the gravitational force is doing work on a 9 kg projectile with velocity directed 34 degrees above the horizontal, we must consider the component of the velocity in the direction of the gravitational force (which is vertical).

Since the gravitational force is downwards, only the vertical component of velocity will contribute to the work done by gravity.

First, resolve the velocity into its horizontal (Vx) and vertical (Vy) components: Vy = V * sin(θ), where V is the magnitudeof the velocity and θ is the angle above the horizontal.Vy = 3.1 m/s * sin(34 degrees) = 1.736 m/s (approx).

The gravitational force (Fg) acting on the projectile is given by the product of the mass (m) and the acceleration due to gravity (g), Fg = m * g.Fg = 9 kg * 9.8 m/s2 = 88.2 N (downwards).

The rate of work done by the gravitational force is the product of this force and the vertical component of velocity, which is Power = Fg * Vy.Power = 88.2 N * 1.736 m/s = 153.01 W (approx).

Thus, the gravitational force is doing work at a rate of approximately 153.01 watts on the projectile at the given instant.