SOLUTION: a ball in thrown vertically up with a velocity of 10m/s. A.determine the time it takes for the ball to reach the maximum height. B. the speed by which the ball will fall back to

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Question 481435: a ball in thrown vertically up with a velocity of 10m/s.
A.determine the time it takes for the ball to reach the maximum height.
B. the speed by which the ball will fall back to the point from where it was thrown.
Found 2 solutions by Alan3354, Earlsdon:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
a ball in thrown vertically up with a velocity of 10m/s.
A.determine the time it takes for the ball to reach the maximum height.
h(t) = -4.9t^2 + 10t
Find the vertex, at t = -b/2a
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B. the speed by which the ball will fall back to the point from where it was thrown.
It's the same, 10 m/sec

Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
The height of an object propelled upwards with an initial velocity from a height is given by the function:
where: is the height (in meters) at time (seconds) , is the initial upward velocity (meters per second), and is the initial height (meters) from which the object is thrown.
A. The graph of this function is a parabola which opens downward and the vertex of the parabola represents the maximum height of the object at time t seconds. So starting with the function:
Substitute m/s and since no initial height was given, we'll assume the ball is thrown from ground-level.

The vertex is found by:
(from )where a = -4.9 and b = 10

seconds. This is the time taken for the ball to reach maximum height.
B. This part of question does not make sense because while the ball is falling, it is accelerating i.e. the speed is not constant!
The question would have to state the time (t) at which the speed of the falling object is required.