In a scene in an action movie, a stunt man jumps from the top of one building to the top of another building 4.4 m away. After a unning start, he leaps at an angle of 17◦ with respect to the flat roof while traveling at a speed of 4.3 m/s.

The acceleration of gravity is 9.81 m/s2 .
To determine if he will make it to the other roof, which is 1.5 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.
Answer in units of m.

distance:

4.4=4.3*cos17*time. Solve for time.
final height
hf=4.3*sin17*time- 1/2 g time^2
solve for hf.

To determine if the stuntman will make it to the other roof, we need to calculate his vertical displacement when he reaches the front edge of the lower building.

First, let's break down the given information:
- Distance between the buildings (horizontal distance): 4.4 m
- Angle of the jump with respect to the flat roof: 17 degrees
- Initial speed (velocity): 4.3 m/s
- Acceleration due to gravity: 9.81 m/s²
- Height difference between the buildings: 1.5 m (lower building is shorter)

To solve this problem, we can use the principles of projectile motion. We need to calculate the vertical displacement, which can be determined by analyzing the vertical and horizontal components of the stuntman's motion.

1. Calculate the initial vertical velocity:
Since we know the initial speed and the angle of the jump, we can calculate the vertical component of the velocity (Viy) using trigonometry:
Viy = initial speed * sin(angle)
Viy = 4.3 m/s * sin(17 degrees)
Viy ≈ 1.25 m/s

2. Calculate the time it takes for the stuntman to travel horizontally:
To find the time of flight, we can use the horizontal distance and the horizontal component of the initial velocity:
Distance = horizontal speed * time
4.4 m = initial speed * cos(angle) * time
time = 4.4 m / (4.3 m/s * cos(17 degrees))
time ≈ 0.95 s

3. Calculate the vertical displacement at the front edge of the lower building:
Using the time of flight (from step 2) and the initial vertical velocity (from step 1), we can calculate the vertical displacement using the equation of motion:
Vertical displacement = Viy * time - (0.5 * g * time²)
Vertical displacement = 1.25 m/s * 0.95 s - (0.5 * 9.81 m/s² * (0.95 s)²)
Vertical displacement ≈ 1.1 m

Therefore, the vertical displacement of the stuntman upon reaching the front edge of the lower building with respect to the taller building is approximately 1.1 meters.

To solve this problem, we need to break down the motion into horizontal and vertical components. Let's start by finding the time it takes for the stuntman to reach the other building.

Step 1: Find the time of flight (T)
Using the formula:
T = (2 * V * sinθ) / g

Given:
V = 4.3 m/s (initial velocity)
θ = 17° (angle of leap)
g = 9.81 m/s^2 (acceleration due to gravity)

Plug in the values to calculate T:
T = (2 * 4.3 * sin(17°)) / 9.81

T ≈ 0.824 s

Step 2: Find the horizontal displacement (x)
Using the formula:
x = V * cosθ * T

Given:
V = 4.3 m/s (initial velocity)
θ = 17° (angle of leap)
T ≈ 0.824 s (time of flight)

Plug in the values to calculate x:
x = 4.3 * cos(17°) * 0.824

x ≈ 3.974 m

Therefore, the horizontal displacement (x) is approximately 3.974 m.

Now, let's find the vertical displacement of the stuntman upon reaching the front edge of the lower building with respect to the taller building.

Step 3: Find the vertical displacement (y)
Using the formula:
y = V * sinθ * T - (1/2) * g * T^2

Given:
V = 4.3 m/s (initial velocity)
θ = 17° (angle of leap)
T ≈ 0.824 s (time of flight)
g = 9.81 m/s^2 (acceleration due to gravity)
h = 1.5 m (height difference between the buildings)

Plug in the values to calculate y:
y = 4.3 * sin(17°) * 0.824 - (1/2) * 9.81 * (0.824)^2

y ≈ 0.785 m

Therefore, the vertical displacement (y) upon reaching the front edge of the lower building with respect to the taller building is approximately 0.785 m.