In a scene in an action movie, a stunt man jumps from the top of one building to the top of another building 5.0 m away. After a running start, he leaps at an angle of 10◦ with respect to the flat roof while traveling at a speed of 5.6 m/s.
The acceleration of gravity is 9.81 m/s2 .
To determine if he will make it to the other roof, which is 3.0 m shorter than the build- ing from which he jumps, find his vertical displacement upon reaching the front edge of the lower building with respect to the taller building.
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To determine the stunt man's vertical displacement upon reaching the front edge of the lower building with respect to the taller building, you can follow these steps:
Step 1: Resolve the initial velocity into its horizontal and vertical components.
Since we know the stunt man's speed and the angle of his jump, we can find the horizontal and vertical components of his velocity:
- The horizontal component (Vx) is given by Vx = V * cos(θ), where V is the speed (5.6 m/s) and θ is the angle (10°).
- The vertical component (Vy) is given by Vy = V * sin(θ), where V is the speed (5.6 m/s) and θ is the angle (10°).
Step 2: Determine the time it takes for the stunt man to reach the other building.
To find the time of flight, we can use the equation: Δy = Vy * t + (1/2) * a * t^2, where Δy is the vertical displacement (which we need to determine), Vy is the vertical component of velocity, a is the acceleration due to gravity (-9.81 m/s^2), and t is the time of flight.
Step 3: Calculate the vertical displacement.
Substituting the known values into the equation from step 2, we have: Δy = Vy * t + (1/2) * a * t^2.
Since the stunt man landed on the other building, his vertical displacement at that point is the height of the landing building minus the height of the starting building.
Step 4: Solve for the vertical displacement.
Using the equation from step 3, plug in the values for Vy, a, and t, and solve for Δy.
Once you have calculated the vertical displacement, you can determine if the stunt man makes it to the other roof by comparing the displacement to the horizontal distance between the buildings.