A ball is thrown horizontally from the top of a cliff 80 m high. How far from the base of the cliff will it land? (Assume g = 10 m/s² and initial horizontal speed = 20 m/s)
Practice Questions
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Q1
A ball is thrown horizontally from the top of a cliff 80 m high. How far from the base of the cliff will it land? (Assume g = 10 m/s² and initial horizontal speed = 20 m/s)
40 m
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80 m
100 m
Time to fall = √(2h/g) = √(2*80/10) = 4 s. Horizontal distance = speed * time = 20 * 4 = 80 m.
Questions & Step-by-step Solutions
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Q: A ball is thrown horizontally from the top of a cliff 80 m high. How far from the base of the cliff will it land? (Assume g = 10 m/s² and initial horizontal speed = 20 m/s)
Solution: Time to fall = √(2h/g) = √(2*80/10) = 4 s. Horizontal distance = speed * time = 20 * 4 = 80 m.
Steps: 9
Step 1: Identify the height of the cliff, which is 80 meters.
Step 2: Use the formula to calculate the time it takes for the ball to fall. The formula is time = √(2h/g), where h is the height and g is the acceleration due to gravity.
Step 3: Plug in the values: h = 80 m and g = 10 m/s². So, time = √(2 * 80 / 10).
Step 4: Calculate the value inside the square root: 2 * 80 = 160, and then 160 / 10 = 16.
Step 5: Now find the square root of 16, which is 4 seconds. This is the time it takes for the ball to hit the ground.
Step 6: Next, calculate the horizontal distance the ball travels while it is falling. Use the formula: distance = speed * time.
Step 7: The initial horizontal speed is given as 20 m/s. So, distance = 20 m/s * 4 s.
Step 8: Multiply 20 by 4 to get the horizontal distance: 20 * 4 = 80 meters.
Step 9: Conclude that the ball will land 80 meters away from the base of the cliff.
