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Ball A is thrown upward with a speed of 35m/s from the ground , while at the same time, another ball B is dropped from a height of 100m with a speed 10m/s along the same straight line . By choosing positive direction of x-axis and origins for position and time, find the height from the ground,where the two balls meet?
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Ball A is thrown upward with a speed of 35m/s from the ground , while ...
Problem
Ball A is thrown upward with a speed of 35m/s from the ground, while at the same time, another ball B is dropped from a height of 100m with a speed 10m/s along the same straight line. By choosing positive direction of x-axis and origins for position and time, find the height from the ground,where the two balls meet?
Solution
Step 1: Analyze the motion of the balls
Ball A is thrown upward with an initial velocity of 35 m/s. The acceleration due to gravity is acting in the opposite direction to the motion of the ball and is equal to 9.8 m/s^2. Ball B is dropped from a height of 100 m with an initial velocity of 10 m/s. The acceleration due to gravity is acting in the downward direction and is equal to 9.8 m/s^2.
Step 2: Find the time taken by the balls to meet
Let t be the time taken by both the balls to meet. The position of ball A after t seconds is given by:
h(A) = 35t - (1/2)gt^2
The position of ball B after t seconds is given by:
h(B) = 100 - 10t - (1/2)gt^2
Since the balls meet at the same height, we can equate h(A) and h(B) and solve for t:
35t - (1/2)gt^2 = 100 - 10t - (1/2)gt^2
Simplifying the equation, we get:
45t = 100
t = 100/45 seconds
Step 3: Find the height at which the balls meet
Substitute the value of t in the equation for h(A) to get the height at which the balls meet:
h(A) = 35(100/45) - (1/2)g(100/45)^2
Simplifying the equation, we get:
h(A) = 77.78 meters
Step 4: Conclusion
Therefore, the two balls meet at a height of 77.78 meters above the ground.
Community Answer
Ball A is thrown upward with a speed of 35m/s from the ground , while ...
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Ball A is thrown upward with a speed of 35m/s from the ground , while at the same time, another ball B is dropped from a height of 100m with a speed 10m/s along the same straight line . By choosing positive direction of x-axis and origins for position and time, find the height from the ground,where the two balls meet?
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