Final answer:
To find the height at which the shell explodes, calculate the initial vertical velocity, use the kinematic equation for vertical motion at the highest point, and rearrange to solve for the height.
Step-by-step explanation:
To calculate the height at which the shell explodes, we must consider the vertical component of the motion separately. Given the initial speed (V0) is 70 m/s and the launch angle (θ) is 75°:
First, find the initial vertical speed (V0y) using V0y = V0 × sin(θ), which gives us V0y = 70 × sin(75°).
Then, use the kinematic equation for vertical motion at the highest point where final velocity (Vy) is 0 m/s: Vy2 = V0y2 - 2gΔh.
Rearrange to find the height (Δh): Δh = V0y2 / (2g).
Substitute V0y and the acceleration due to gravity (g = 9.8 m/s2) to find the height at which the shell explodes.
The final answer for the height will be calculated by using the previously mentioned steps.