7. + \"M points SerCP11 3.PO34. Miy Notes Ask Your Teacher You can use any coord

Question

7. + "M points SerCP11 3.PO34. Miy Notes Ask Your Teacher You can use any coordinate system you like in order to solve a projectile motion problem. To demonstrate the truth of this statement, consider a ball thrown off the top of a building with a velocity v at an angle with respect to the horizontal. Let the building be 41.0 m tall, the initial horizontal velocity be 8.70 m/s, and the initial vertical velocity be 10.5 m/s. Choose your coordinates such that the positive y-axis is upward, and the x-axis is to the right, and the origin is at the point where the ball is released. (a) With these choices, find the ball's maximum height above the ground and the time it takes to reach the maximum height. maximum height above ground time to reach maximum height (b) Repeat your calculations choosing the origin at the base of the building maximum height above ground time to reach maximum height

Explanation / Answer

Apply kinematic equation

The vertical displacement from the launch point to the top of the arc is

vy^2 = vo^2 +2 ay del y

dely = v^2 - vo^2 / 2 ay

= 0-10.5^2/ 2(-9.8)

=5.625 m

y max = yo + del y

If the origin is chosen at the top of the building, then y0 = 0

y max = 5.625 m

Thus, the maximum height above the ground is

h max = 41 m + 5.625 m = 46.625 m

The elapsed time from the point of release to the top of the arc is found from

v= u+ at

t= vy- voy/ ay

= 0 - 10.5/-9.8 = 1.071 s

(b)

If the origin is chosen at the base of the building (ground level),

hmax = yo + del y = 41 + 5.625 m= 46.625 m

v= u+ at

t= vy- voy/ ay

= 0 - 10.5/-9.8 = 1.071 s

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