A rocket is fired at a speed of 74.0 m/s from ground level, at an angle of 68.0 ° above the horizontal. The rocket is fired toward an 49.8-m high wall, which is located 32.0 m away. The rocket attains its launch speed in a negligibly short period of time, after which its engines shut down and the rocket coasts. By how much does the rocket clear the top of the wall?
How can a school subject called Henry Ford be about rockets?
Henry Ford manufactured autos, trucks, tractors, and airplanes. He did not manufacture rockets.
"henry ford" -- is that the name of your school?
"physics" is what belongs in the School Subject box.
To find out how much the rocket clears the top of the wall, we first need to calculate the time it takes for the rocket to reach the wall.
We can break down the initial velocity of the rocket into its horizontal and vertical components. The horizontal component is given by: Vx = V * cos(θ), where V is the launch speed and θ is the angle above the horizontal.
Vx = 74.0 m/s * cos(68.0°)
Vx = 74.0 m/s * 0.389
Vx = 28.786 m/s (rounded to three decimal places)
The vertical component is given by: Vy = V * sin(θ).
Vy = 74.0 m/s * sin(68.0°)
Vy = 74.0 m/s * 0.920
Vy = 68.080 m/s (rounded to three decimal places)
Since there is no acceleration in the horizontal direction, the time taken to reach the wall can be calculated using the horizontal distance traveled, which is 32.0 m.
Time = Distance / Velocity
Time = 32.0 m / 28.786 m/s = 1.111 s (rounded to three decimal places)
Now, we can calculate the maximum height reached by the rocket using the vertical component of velocity. We'll use the equation:
Vertical Displacement = Vy_initial * Time + (0.5 * gravity * time^2)
Where gravity is the acceleration due to gravity, approximately 9.8 m/s².
Vertical Displacement = 68.080 m/s * 1.111 s + (0.5 * 9.8 m/s² * (1.111 s)^2)
Vertical Displacement = 75.643 m (rounded to three decimal places)
Finally, we can determine how much the rocket clears the top of the wall by subtracting the height of the wall (49.8 m) from the maximum vertical displacement.
Clearance = Vertical Displacement - Wall Height
Clearance = 75.643 m - 49.8 m = 25.843 m (rounded to three decimal places)
Therefore, the rocket clears the top of the wall by approximately 25.843 meters.