Answer:
To find the height at which the grappling hook will hit the wall, we need to use the equations of motion and trigonometry.
First, let's break down the given information:
- The initial velocity of the grappling hook is 35.7 m/s.
- The angle at which it is shot up is 52° from the ground.
- Mr. F stands 13 meters away from the wall.
Now, we can calculate the vertical and horizontal components of the initial velocity. To do this, we use trigonometry. The vertical component can be found by multiplying the initial velocity by the sine of the angle: 35.7 m/s * sin(52°) ≈ 28.08 m/s. The horizontal component can be found by multiplying the initial velocity by the cosine of the angle: 35.7 m/s * cos(52°) ≈ 21.92 m/s.
Next, let's find the time it takes for the grappling hook to reach the wall. We can use the horizontal component of the initial velocity and the distance to the wall. The time can be calculated using the formula: time = distance / velocity. So, time = 13 m / 21.92 m/s ≈ 0.593 seconds.
Now, we can find the height at which the grappling hook will hit the wall. We can use the formula for vertical motion: height = initial vertical velocity * time - (1/2) * acceleration * time^2. Since the grappling hook is shot vertically upwards, the acceleration is the acceleration due to gravity, which is approximately 9.8 m/s^2. Plugging in the values, we get: height = 28.08 m/s * 0.593 s - (1/2) * 9.8 m/s^2 * (0.593 s)^2 ≈ 8.3 meters.
Therefore, the grappling hook will hit the wall at a height of approximately 8.3 meters.