A 0.25 kg skeet (clay target) is fired at an angle of 30 degrees to the horizon with a speed of 25 m/s. When it reaches the maximum height, it is hit from below by a 15 g pellet travelling upward at a speed of 200 m/s. The pellet is embedded in the skeet. (a) How much higher did the skeet go up? (b) How much extra distance does the skeet travel because of the collision?

does this problem involve projectile motion?

Yes, it is a projectile motion problem, with conservation of momentum thrown in at the peak.

so how do i answer this? :) pls. and thank you

Yes, this problem does involve projectile motion. Projectile motion refers to the motion of an object that is launched into the air and moves along a curved path under the influence of gravity, without any additional propulsion. In this case, both the skeet and the pellet are examples of projectiles, and their motions are influenced by the force of gravity.

To solve this problem, we can break it down into several steps:

Step 1: Find the initial vertical and horizontal velocities of the skeet.
Given that the skeet is fired at an angle of 30 degrees to the horizon with a speed of 25 m/s, we can use trigonometry to determine its initial vertical and horizontal velocities.

Vertical velocity (Vy) = initial speed (v) * sin(theta)
Horizontal velocity (Vx) = initial speed (v) * cos(theta)

Where:
- initial speed (v) is 25 m/s
- theta is the angle of 30 degrees

Step 2: Calculate the time it takes for the skeet to reach its maximum height.
To find the time it takes for the skeet to reach its maximum height, we can use the vertical motion equation:

Vy = Vf - g * t

Where:
- Vy is the vertical velocity (which is initially positive)
- Vf is the final vertical velocity (which is 0 m/s at the maximum height)
- g is the acceleration due to gravity (approximately -9.8 m/s^2)
- t is the time

Step 3: Determine the height reached by the skeet.
Using the time calculated in Step 2 and the initial vertical velocity, we can find the height reached by the skeet using the vertical motion equation:

Δy = Vy * t + (1/2) * g * t^2

Where:
- Δy is the vertical displacement (height)
- Vy is the initial vertical velocity
- t is the time

(a) So, to find how much higher the skeet goes up, you can calculate the horizontal distance traveled by the skeet alone and find the height at that horizontal distance using the equations mentioned above.

(b) To find the extra distance traveled by the skeet due to the collision, you can calculate the horizontal displacement using the initial horizontal velocity and the time it takes for the pellet to reach the skeet.

Let's proceed with these calculations to find the answers.