A 70 kg waterslide rider traveling at 15 meters per second hits a ramp with a 58 degree launch angle - How high will they fly?
To determine how high the rider will fly on the water slide ramp, we can use the principles of projectile motion. Let's break down the problem into manageable steps:
Step 1: Calculate the vertical component of the rider's initial velocity.
The vertical component is the initial velocity of the rider multiplied by the sine of the launch angle.
Vertical component = Initial velocity * sin(Launch angle)
Step 2: Calculate the time it takes for the rider to reach the highest point.
The time it takes for the rider to reach the highest point is determined solely by the vertical motion.
You can use the following equation to find the time: Time to reach highest point = (Vertical component of Initial velocity) / (acceleration due to gravity)
Step 3: Calculate the maximum height reached by the rider.
The maximum height reached can be calculated using the following equation: Maximum height = (Vertical component of Initial velocity)^2 / (2 * acceleration due to gravity)
Now, let's calculate the values for each step:
Given:
Mass of the rider (m) = 70 kg
Initial velocity (u) = 15 m/s
Launch angle (θ) = 58 degrees
Acceleration due to gravity (g) = 9.8 m/s^2
Step 1: Calculate the vertical component of the initial velocity.
Vertical component = 15 m/s * sin(58 degrees) ≈ 12.58 m/s
Step 2: Calculate the time to reach the highest point.
Time to reach highest point = 12.58 m/s / 9.8 m/s^2 ≈ 1.28 s
Step 3: Calculate the maximum height reached.
Maximum height = (12.58 m/s)^2 / (2 * 9.8 m/s^2) ≈ 8.06 m
Therefore, the rider will reach a maximum height of approximately 8.06 meters on the water slide ramp.