In a scene in an action movie, a stuntman jumps from the top of one building to the top of another building 4.0 m away. After a running start, he leaps at a velocity of 5.0m/s at an angle of 15 degrees with respect to the flat roof. Will he make it to the other roof, which is 2.5 m shorter than the building he jumps from?
-2.3m
yes, he will be able to make it to the other roof.
I wish I knew
To determine if the stuntman will make it to the other roof, we need to analyze the motion of the jump. We can break down the motion into horizontal and vertical components.
First, let's consider the vertical motion. We need to find out the time it takes for the stuntman to reach the other building. We can use the equation:
h = v₀*t + (1/2)*g*t²
Where:
h = height of the jump
v₀ = initial vertical velocity (in this case, v₀ = 5.0 m/s * sin(15°))
g = acceleration due to gravity (approximately 9.8 m/s²)
t = time of flight
Since the difference in height between the buildings is given as 2.5 m, we can rewrite the equation as:
2.5 = (5.0 * sin(15°)) * t - (1/2) * 9.8 * t²
This equation is quadratic in terms of time (t). We can rearrange it to get a quadratic equation in standard form:
-4.9 * t² + (5.0 * sin(15°)) * t - 2.5 = 0
We can solve this equation to find the value(s) of t. Using the quadratic formula:
t = (-b ± √(b² - 4ac)) / (2a)
Where:
a = -4.9
b = 5.0 * sin(15°)
c = -2.5
Solving for t, we get two possible values: t ≈ 0.449 s and t ≈ 0.874 s.
Now, let's analyze the horizontal motion. We need to find out the horizontal distance covered by the stuntman during this time. We can use the equation:
d = v₀x * t
Where:
d = horizontal distance
v₀x = initial horizontal velocity (in this case, v₀x = 5.0 m/s * cos(15°))
t = time of flight (we will consider the larger value, t ≈ 0.874 s)
Using the given values, we can calculate the horizontal distance covered:
d = (5.0 * cos(15°)) * 0.874 ≈ 4.0 m
The calculated horizontal distance covered is essentially equal to the distance between the buildings, which means the stuntman will barely make it to the other roof.