In a scene in an action movie, a stunt man jumps from the top of one building to the top of another building 3.5 m away. After a running start, he leaps at an angle of 14� 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 2.2 m shorter than the building 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. (Help! Thanks!)
His horizontal speed is 5.6 cos 14° = 5.4337m/s
So, to cross the 3.5m between buildings, it will take 3.5/5.4337 = 0.644s
So, how far does he fall in .644 sec?
s = 1/2 at² = 4.905 * .644² = 2.03m
Looks like he'll make it.
Hello, Steve. Thanks for help, but I'm sorry that your answer is incorrect. I had tried your answer， but it said incorrect.
To determine if the stuntman will make it to the other roof, we need to find his vertical displacement upon reaching the front edge of the lower building with respect to the taller building.
First, we can break down the motion into horizontal and vertical components.
Horizontal component:
The stuntman jumps 3.5 m away, so the horizontal displacement is 3.5 m.
Vertical component:
We can use the equation of motion in the vertical direction:
vf^2 = vi^2 + 2as
where:
vf = final velocity in the vertical direction (0 m/s at the top of the jump)
vi = initial velocity in the vertical direction
a = acceleration due to gravity (-9.81 m/s^2)
s = displacement in the vertical direction (unknown)
Since the vertical displacement is unknown, we can use the equation:
vf^2 = vi^2 + 2as
0^2 = vi^2 - 2(9.81 m/s^2)s
vi^2 = 19.62s (equation 1)
We can also use the equation of motion to relate the vertical displacement s to the initial velocity in the vertical direction and the angle of the jump:
s = vi*t + (1/2)*a*t^2
where:
t = time of flight
We can find the time of flight using the horizontal displacement and the horizontal velocity. The horizontal displacement is 3.5 m, and the horizontal velocity can be found as follows:
vix = vi * cos(θ)
where:
θ = angle of the jump (14 degrees)
vix = horizontal velocity
Substituting the given values:
3.5 m = (5.6 m/s) * cos(14 degrees) * t
3.5 m = 5.6 m/s * 0.9703 * t
t = 3.5 m / (5.6 m/s * 0.9703)
t ≈ 0.637 s
Now, we can substitute the time of flight into the equation for vertical displacement:
s = vi*t + (1/2)*a*t^2
s = (5.6 m/s * sin(14 degrees)) * 0.637 s + (1/2) * (-9.81 m/s^2) * (0.637 s)^2
s = 2.626 m - 2.546 m
s ≈ 0.080 m
Therefore, the vertical displacement upon reaching the front edge of the lower building with respect to the taller building is approximately 0.080 m.
To determine if the stuntman will make it to the other roof, we need to calculate his vertical displacement upon reaching the front edge of the lower building with respect to the taller building.
1. Start by breaking down the given information:
Distance between the buildings (horizontal displacement): 3.5 m
Angle of the jump with respect to the flat roof: 14 degrees
Speed of the stuntman: 5.6 m/s
Acceleration due to gravity: 9.81 m/s^2
Height difference between the buildings: 2.2 m (lower building is 2.2 m shorter)
2. Resolve the initial velocity into horizontal and vertical components using trigonometry:
Initial vertical velocity (Vy) = Initial speed (5.6 m/s) * sin(angle)
Initial horizontal velocity (Vx) = Initial speed (5.6 m/s) * cos(angle)
3. Calculate the time of flight:
Vertical displacement (y) = Vy * time + (1/2) * gravity * time^2 (since y = Vyt + 1/2gt^2)
Here, y = -2.2 m (negative because the lower building is shorter)
Initial vertical position (y0) = 0 (starting from the top of the taller building)
Acceleration due to gravity (a) = -9.81 m/s^2 (negative because it opposes the direction)
Substitute the values and solve for time (t).
4. Calculate the horizontal displacement at the time of flight:
Horizontal displacement (x) = Vx * t
5. Check if the horizontal displacement is equal to or greater than the distance between the buildings:
If x >= 3.5 m, then the stuntman will make it to the other roof.
Now, let's calculate it step by step.
Step 2:
Vy = 5.6 m/s * sin(14 degrees)
Vx = 5.6 m/s * cos(14 degrees)
Step 3:
Using the quadratic equation, -2.2 = (0.5 * (-9.81) * t^2) + (Vy * t)
Solve the equation to find the value of t.
Step 4:
x = Vx * t
Step 5:
Check if x >= 3.5 m to determine if the stuntman will make it to the other roof.