A ball is thrown straight upward from ground level. At what speed must the ball be thrown if it is to reach a maximum height 21 meters above the ground?
20.28792744 m/s
thanks for nothing i solved it myself
To find the required speed at which the ball must be thrown in order to reach a maximum height of 21 meters, we can use the principles of projectile motion.
Let's breakdown the problem and solve it step by step:
Step 1: Determine the acceleration due to gravity
The acceleration due to gravity near the surface of the Earth is approximately 9.8 m/s². This means that as the ball is thrown upward, it will experience a constant downward acceleration of 9.8 m/s².
Step 2: Calculate the time it takes to reach maximum height
When the ball reaches its maximum height, its vertical velocity will be zero since it momentarily comes to a stop before reversing direction and falling back down. We can use the following equation to find the time it takes to reach the maximum height:
v = u + at
Here, v is the final velocity (zero in this case), u is the initial velocity, a is the acceleration due to gravity (-9.8 m/s²), and t is the time taken.
Since the final velocity is zero, let's rearrange the equation:
0 = u - 9.8t
Solving for t, we get:
t = u/9.8
Step 3: Calculate the maximum height
To find the maximum height reached by the ball, we can use the following equation:
h = ut + (1/2)at²
Here, h is the maximum height, u is the initial velocity, a is the acceleration due to gravity (-9.8 m/s²), and t is the time taken.
Substituting the value of time from Step 2, we get:
h = u(u/9.8) + (1/2)(-9.8)(u/9.8)²
Simplifying the equation, we have:
h = u²/19.6
Since we want the maximum height to be 21 meters, we can set up the following equation:
21 = u²/19.6
Multiplying both sides by 19.6, we get:
413.6 = u²
Taking the square root of both sides, we find:
u = √413.6 ≈ 20.33 m/s
Therefore, the ball must be thrown with a speed of approximately 20.33 m/s to reach a maximum height of 21 meters above the ground.