DIRECTIONS: Read and analyze each question carefully. Solve the following problems. Write your solutions on the space provided. (10pts each)A golf ball is thrown horizontally from a window that is 20m high with a velocity of 10m/s. FindHow long does a ball take to reach the ground?How fast will the ball hit the gorund?a:Given:Asked:Solution:
Question
DIRECTIONS: Read and analyze each question carefully. Solve the following problems. Write your solutions on the space provided. (10pts each)A golf ball is thrown horizontally from a window that is 20m high with a velocity of 10m/s. FindHow long does a ball take to reach the ground?How fast will the ball hit the gorund?a:Given:Asked:Solution:
Solution
a:
Given: Height (h) = 20m Initial horizontal velocity (u) = 10m/s Acceleration due to gravity (g) = 9.8m/s²
Asked:
- Time taken to reach the ground
- Final velocity when it hits the ground
Solution:
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We can use the equation of motion to find the time taken to reach the ground. The equation is h = ut + 0.5gt². Since the ball is thrown horizontally, the initial vertical velocity (u) is 0. So, the equation becomes h = 0.5gt². We can rearrange this to find t (time) = sqrt(2h/g) = sqrt((2*20)/9.8) = 2.02 seconds.
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The final velocity can be found using the equation v = u + gt. Again, since the ball is thrown horizontally, the initial vertical velocity (u) is 0. So, the equation becomes v = gt = 9.8*2.02 = 19.8 m/s.
However, this is only the vertical component of the velocity. The horizontal component remains constant at 10 m/s. We can find the resultant velocity using Pythagoras' theorem: sqrt((horizontal velocity)² + (vertical velocity)²) = sqrt((10)² + (19.8)²) = 22.14 m/s.
So, the ball takes approximately 2.02 seconds to reach the ground and it will hit the ground with a velocity of approximately 22.14 m/s.
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