Calculate Vertical Displacement in Stunt Jump | 2D Motion Physics Problem

[wwommack]

Homework Statement

In a scene in an action movie, a stunt man
jumps from the top of one building to the
top of another building 4.8 m away. After a
running start, he leaps at an angle of 11◦ with
respect to the flat roof while traveling at a
speed of 5.4 m/s.
The acceleration of gravity is 9.81 m/s2 .
To determine if he will make it to the other
roof, which is 1.7 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.

Homework Equations

acceleration formula

The Attempt at a Solution

tried and got a crazy number

 

[kuruman]

Please be more specific if you want us to help you. Show us what formula you used, how you used it and what numbers you got.

 

[tomcue]

, need help

I would approach this problem by breaking it down into its components and using the appropriate equations and principles to solve it.

First, we can draw a diagram to visualize the scenario described in the problem. We have a horizontal distance of 4.8 m and a vertical height difference of 1.7 m between the two buildings. The stunt man's initial speed is 5.4 m/s and he jumps at an angle of 11 degrees.

Next, we can use the equations of motion to analyze the vertical displacement of the stunt man. We know that the acceleration due to gravity is acting on the stunt man during his jump, and we can use the formula:

d = v0t + 1/2at^2

where d is the vertical displacement, v0 is the initial velocity, a is the acceleration due to gravity, and t is the time.

Since we are only interested in the vertical displacement, we can use the component of the initial velocity in the vertical direction, which is given by v0y = v0sin(θ), where θ is the angle of the jump. Thus, we have:

d = (v0sin(θ))t + 1/2at^2

We can also use the fact that the time of flight, t, is equal to the total horizontal distance divided by the horizontal velocity, which is given by v0cos(θ). So, we have:

t = 4.8 m / (5.4 m/s * cos(11°)) = 0.828 s

Substituting this value of t into our previous equation, we get:

d = (5.4 m/s * sin(11°)) * 0.828 s + 1/2 * (9.81 m/s^2) * (0.828 s)^2 = 1.66 m

Therefore, the vertical displacement of the stunt man upon reaching the front edge of the lower building is 1.66 m. This means that he will clear the 1.7 m height difference and make it to the other roof.

As a scientist, it is important to carefully analyze a problem and use the appropriate equations and principles to solve it. It is also important to double check the calculations and units to ensure accuracy. In this case, the units of the final answer are in meters, which is consistent with the units of the