A circus performer wants to land in a net 5 meters to the right of where she will let go of the trapeze. If she is 10 meters above the net, how fast must she be moving horizontally when she lets go?
How long will it take to fall 10 m?
Given that time, velocity=5m/time
To find out how fast the circus performer must be moving horizontally when she lets go, we can use the principles of projectile motion. Let's break down the given information:
- The performer wants to land in a net 5 meters to the right of where she let go.
- The performer is 10 meters above the net.
Now, let's determine the steps to find the required horizontal speed:
Step 1: Determine the time of flight
When an object is thrown vertically upwards and lands back at the same height, the time taken to reach the highest point is the same as the time taken to fall back down. In this case, the time of flight can be found using the following formula:
t = sqrt((2h) / g)
where:
t = time of flight
h = initial vertical height
g = acceleration due to gravity (approximately 9.8 m/s^2)
Plugging in the values:
t = sqrt((2 * 10) / 9.8)
t ≈ 1.43 seconds
Step 2: Determine the horizontal distance traveled during the time of flight
Since the horizontal speed remains constant throughout the motion, the horizontal distance traveled can be found using the formula:
d = v * t
where:
d = horizontal distance
v = horizontal velocity
t = time of flight (found earlier)
We need to find the horizontal distance traveled, which is 5 meters. Rearranging the formula, we can solve for v:
v = d / t
v = 5 / 1.43
v ≈ 3.50 m/s
Therefore, the circus performer must be moving horizontally at approximately 3.50 m/s when she lets go of the trapeze to land 5 meters to the right of the net.