superman is said to be able to leap tall buildings in a single bound. how high a building could superman jump over if he were to leave the ground with a speed of 60m/s at an angle of 75 degrees to the horizontal?
i have the same question
To determine how high a building Superman could jump over, we can use basic principles of projectile motion. Let's break it down step by step:
Step 1: Separate the Initial Velocity
The initial velocity can be separated into horizontal and vertical components. The horizontal component (Vx) remains constant during the entire motion, while the vertical component (Vy) changes over time due to gravity.
Given the angle of 75 degrees to the horizontal and an initial speed of 60 m/s, we can find the horizontal and vertical components of the velocity.
Vx = 60 m/s * cos(75°)
Vy = 60 m/s * sin(75°)
Now we can calculate these values:
Vx = 60 m/s * cos(75°) = 15.45 m/s (approx.)
Vy = 60 m/s * sin(75°) = 57.71 m/s (approx.)
Step 2: Calculate the Time of Flight
To determine the time it takes for Superman to reach the peak of his jump, we can use the vertical component of his velocity (Vy) and the acceleration due to gravity (g), which is approximately 9.8 m/s^2.
Using the equation:
Vy = gt
Where:
g = 9.8 m/s^2 (acceleration due to gravity)
t = time
We can rearrange the equation to solve for time (t):
t = Vy / g
Substituting the values:
t = 57.71 m/s / 9.8 m/s^2
t ≈ 5.89 seconds (approx.)
Step 3: Determine the Height of the Building
Now we can use the time of flight calculated previously to find the height of the building. Since we know the time it takes for Superman to reach the peak and descend, we can calculate the height using the vertical velocity (Vy) and time (t) values.
Using the equation:
h = Vy * t - 0.5 * g * t^2
Where:
h = height of the building
Substituting the values and solving for h:
h = (57.71 m/s) * (5.89 s) - 0.5 * (9.8 m/s^2) * (5.89 s)^2
h ≈ 169.27 meters (approx.)
Therefore, if Superman were to leave the ground with a speed of 60 m/s at an angle of 75 degrees to the horizontal, he could jump over a building approximately 169.27 meters high.