To determine whether the rock will reach the top of the wall, we need to compare the maximum height reached by the rock with the height of the wall.
The initial height of the rock above the ground is 1.55 m, and it needs to reach a height of 3.65 m to reach the top of the wall.
The maximum height reached by a projectile can be calculated using the formula:
H = (V₀² * sin²(θ)) / (2 * g)
where: H is the maximum height reached, V₀ is the initial velocity of the projectile, θ is the launch angle, and g is the acceleration due to gravity.
In this case, the initial velocity is 7.40 m/s, and the launch angle is 90 degrees since the rock is thrown straight up. The acceleration due to gravity is approximately 9.8 m/s².
Plugging in the values, we have:
H = (7.40² * sin²(90°)) / (2 * 9.8) H = (54.76 * 1) / 19.6 H ≈ 2.80 m
The maximum height reached by the rock is approximately 2.80 m. Since this is less than the height of the wall (3.65 m), the rock will not reach the top of the wall.