a. The skeet goes up approximately 10.47 meters before the collision.
b. The skeet travels approximately 300.76 meters extra due to the collision.
a. To determine how much higher the skeet goes up, we need to calculate the maximum height it reaches before the collision. We can use the projectile motion equations.
First, let's find the initial vertical velocity component of the skeet (v0y). We can calculate this using the given launch angle (θ) and the initial velocity (vo):
v0y = vo * sin(θ)
v0y = 28.9 m/s * sin(29.2°)
v0y = 14.3 m/s
Next, we can calculate the time it takes for the skeet to reach the maximum height. At this point, the vertical velocity component becomes zero (vy = 0). We can use the equation:
vy = v0y + gt
0 = 14.3 m/s + (-9.8 m/s^2) * t
t = 1.46 seconds
Using this time, we can find the maximum height (h) using the equation:
h = v0y * t + (1/2) * g * t^2
h = 14.3 m/s * 1.46 seconds + (1/2) * (-9.8 m/s^2) * (1.46 seconds)^2
h = 10.47 meters
Therefore, the skeet goes up approximately 10.47 meters.
b. To find the extra distance the skeet travels due to the collision, we need to calculate the horizontal displacement (Δx) of the pellet before it hits the skeet.
The time it takes for the pellet to reach the skeet is the same as the time it took for the skeet to reach the maximum height (1.46 seconds).
Using the horizontal velocity of the pellet (206 m/s) and the time, we can calculate the horizontal displacement:
Δx = v * t
Δx = 206 m/s * 1.46 seconds
Δx ≈ 300.76 meters
Therefore, the skeet travels approximately 300.76 meters extra because of the collision.