maria throws a ball straight up with an initial velocity of 10m/s what is its velocity at the highest point?
Trick question. At its highest point, the ball changes direction. It has to stop to do that.
v = 0
To determine the velocity of the ball at the highest point, we need to consider the motion of the ball when it is thrown straight up.
At the highest point of the ball's motion, its vertical velocity becomes zero momentarily before it starts falling back down due to the force of gravity. This is because the upward velocity decreases as the ball goes against gravity until it reaches zero at the highest point.
Knowing that the initial velocity of the ball is 10 m/s and assuming no air resistance, we can use the following equation to calculate the highest point velocity:
v_f = v_i + at
Where:
- v_f is the final velocity at the highest point (what we're trying to find)
- v_i is the initial velocity of the ball (10 m/s)
- a is the acceleration due to gravity, which is approximately -9.8 m/s^2 (negative sign indicating downward direction)
- t represents the time it takes for the velocity to change from the initial velocity to zero at the highest point
Since the ball reaches its highest point, the displacement in the vertical direction becomes zero. Using the equation for displacement, we can find the time it takes for the ball to reach the highest point:
s = v_i * t + (1/2) * a * t^2
In this case, since the displacement is zero, the equation simplifies to:
0 = v_i * t + (1/2) * a * t^2
We can substitute the given values into this equation and solve for t. Then, we can substitute the calculated value of t back into the first equation to find the final velocity at the highest point (v_f).
Let's calculate it step by step:
1. Calculate the time it takes for the ball to reach the highest point (t):
0 = 10 * t + (1/2) * (-9.8) * t^2
This equation is a quadratic equation. You can solve it by factoring, completing the square, or using the quadratic formula.
Assuming we solve it using the quadratic formula:
t = (-10 ± √((10^2) - 4 * (-9.8/2) * 0)) / (2 * (-9.8/2))
By simplifying the equation above, we get:
t = (-10 ± √(100 + 9.8 * 0)) / (-9.8)
t = (-10 ± √100) / (-9.8)
Since we're dealing with time, we can ignore the negative value of t, so:
t = (-10 + 10) / (-9.8)
t = 0 / (-9.8)
t = 0
Therefore, it took 0 seconds for the ball to reach the highest point.
2. Calculate the final velocity at the highest point (v_f):
v_f = v_i + at
v_f = 10 + (-9.8) * 0
v_f = 10 + 0
v_f = 10 m/s
Thus, the velocity of the ball at the highest point is 10 m/s. The ball momentarily stops before changing direction and coming back down.