Divers at Acapulco dive from a cliff that is 60 m high. If the rocks below the cliff extend outward for 23 m, what is the minimum horizontal velocity a diver must have to clear the rocks safely?
You are at a Marlins baseball game with your friend, who won a pair of tickets for seats just behind the right field wall 120 m from home plate. Jose Reyes hits a long fly ball at a 41.0° angle from the horizontal and you catch it 3.59 s later for a home run. What was the inital speed with which the ball was hit? (m/s)
To determine the minimum horizontal velocity a diver must have to clear the rocks safely, we can use the concept of projectile motion.
The key idea is that the horizontal motion and vertical motion of the diver are independent of each other. The horizontal velocity remains constant throughout the motion, while the vertical motion is influenced by gravity.
Let's break down the problem step by step:
1. First, we need to find the time it takes for the diver to fall from the top of the cliff to the height of the rocks. We can use the vertical motion equation:
h = ut + (1/2)gt^2,
where h is the vertical distance (height), u is the initial vertical velocity (which is 0 since the diver starts from rest at the top), g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time.
Plugging in the values, we have:
23 = 0*t + (1/2)*9.8*t^2.
Simplifying the equation, we get:
4.9t^2 = 23.
Solving for t, we find:
t ≈ 2.42 seconds.
2. Now that we know the time it takes for the diver to fall to the height of the rocks, we can find the minimum horizontal velocity required to clear the rocks.
The horizontal distance traveled by the diver can be calculated using:
d = vt,
where d is the horizontal distance, v is the horizontal velocity, and t is the time.
Plugging in the values, we have:
60 = v*2.42.
Solving for v, we find:
v ≈ 24.79 m/s.
Therefore, the minimum horizontal velocity a diver must have to clear the rocks safely is approximately 24.79 m/s.