In a chase scene, a movie stuntman runs horizontally off the flat roof of one building and lands on another roof 2.0m lower.
If the gap between the buildings is 4.4m wide, how fast must he run to cross the gap?
Express your answer to two significant figures and include the appropriate units.
Ignoring air friction ( I wish I could have done that when I was a long jumper in HSchool).
hf=hi+ 1/2 g t^2
-2=0-4.9 t^2 solve for time in air, t.
horizontal distance:
4.4=v*t solve for v.
To find the speed needed by the stuntman to cross the gap, we can use the principles of projectile motion.
First, let's assume that the stuntman launches himself at an angle of 45 degrees with respect to the horizontal.
We can break down the motion into horizontal and vertical components. The horizontal component will determine the speed needed.
1. Calculate the horizontal component of the displacement:
The horizontal displacement is equal to the width of the gap between the buildings, which is 4.4 m.
2. Calculate the vertical component of the displacement:
The stuntman jumps from one building to another, so the vertical displacement is the height difference between the two roofs, which is 2.0 m downwards.
3. Find the time of flight:
Using the vertical component, we can calculate the time it takes for the stuntman to cover the vertical displacement using the formula:
Vertical displacement (Δy) = (0.5) * g * t^2
Where g is the acceleration due to gravity (9.8 m/s^2) and t is the time of flight.
Rearranging the formula, we get:
t = √(2 * Δy / g)
t = √(2 * 2.0 / 9.8)
t = √(0.41)
t ≈ 0.64 seconds
4. Calculate the speed needed:
The horizontal distance covered is equal to the horizontal velocity (Vx) multiplied by the time of flight (t).
Horizontal displacement = Vx * t
Rearranging the formula, we get:
Vx = Horizontal displacement / t
Vx = 4.4 / 0.64
Vx = 6.88 m/s
Therefore, the stuntman must run at a speed of approximately 6.88 m/s (or 6.9 m/s to two significant figures) to cross the gap between the buildings.
To determine the speed at which the movie stuntman must run to cross the gap between the buildings, we can use the principle of conservation of energy.
Let's start by considering the energy of the stuntman at his starting position. At the roof's edge, he possesses only potential energy, given by the equation:
Potential energy = m * g * h
Where:
m is the mass of the stuntman (which we can assume cancels out),
g is the acceleration due to gravity (9.8 m/s^2), and
h is the height from the ground (2.0 m).
The potential energy can also be expressed as:
Potential energy = m * g * h = (1/2) * m * v^2
Where:
v is the velocity of the stuntman.
Since we're looking for the velocity, we can rewrite the equation as:
v = √(2 * g * h)
Substituting the given values:
v = √(2 * 9.8 * 2.0)
Calculating this expression:
v ≈ √(39.2)
Rounding the result to two significant figures:
v ≈ 6.3 m/s
Therefore, to cross the gap between the buildings, the stuntman must run at a speed of approximately 6.3 m/s.