An egg is thrown nearly vertically upward from a point near the cornice of a tall building. It just misses the cornice on the way down and passes a point 8.5 m below its starting point 3.0 s after it leaves the thrower’s hand. Air resistance may be ignored.
(c) What is the magnitude of the velocity at the highest point?
c) zero. It stops before coming down.
To find the magnitude of the velocity at the highest point, we can use the equations of motion. In this case, we will use the equation for vertical motion with constant acceleration:
v = u + gt
Where:
v = final velocity (at the highest point)
u = initial velocity (when the egg is thrown upward)
g = acceleration due to gravity
t = time taken to reach the highest point
Since the egg is thrown upward, the initial velocity (u) will be positive. We are given the time taken to reach the point below the starting point, which is 3.0 seconds. We also know that the acceleration due to gravity is approximately 9.8 m/s^2.
First, we need to find the initial velocity (u). We know that the egg passes a point 8.5 m below its starting point 3.0 s after it is thrown. Therefore, we can use the equation of motion:
s = ut + (1/2)gt^2
Rearranging the equation, we get:
u = (s - (1/2)gt^2) / t
Substituting the given values, we have:
u = (8.5 m - (1/2)(9.8 m/s^2)(3.0 s)^2) / 3.0 s
After calculating the above expression, we get the value of the initial velocity (u).
Once we have the value of the initial velocity (u), we can use the equation of motion for vertical motion to find the final velocity (v) at the highest point.
Using the equation:
v = u + gt
Substituting the known values, we have:
v = u + (9.8 m/s^2)(t)
Since the velocity at the highest point is zero (the egg momentarily comes to rest), we can set the final velocity (v) to zero and solve for t:
0 = u + (9.8 m/s^2)(t)
After calculating the above expression, we get the value of the time (t) taken to reach the highest point.
Finally, we can substitute the time (t) into the equation v = u + gt to find the magnitude of the velocity (v) at the highest point.