Instant Target
Posted in Anti-Aging by admin
You are to throw a ball with a speed of 15.5 m/s at a target that is height h = 4.50 m?
the height (h = 4.50 m) is above the level at which you release the ball. You want the ball’s velocity to be horizontal at the instant it reaches the target.
At what angle θ above the horizontal must you throw the ball?
in degrees
(b) What is the horizontal distance from the release point to the target?
in meters
(c) What is the speed of the ball just as it reaches the target?
in m/s
a. The vertical velocity component of the ball must be 0 when it reaches the target so the velocity will only have a horizontal component at that time.
Call the initial vertical component v0. So:
v = v0 – gt = v0 – 9.8t = 0
t = (v0/9.8)
Thd distance upward travelled by the ball must be 4.5 meters so use the distance formula:
s = v0*t – (1/2)gt^2
4.5 = v0*t – 4.9t^2
4.9t^2 – v0*t + 4.5 = 0
Substitute the expession for t from above:
(v0)^2/(2*9.8) – (v0)^2/9.8 + 4.5 = 0
(v0)^2/(2*9.8) = 4.5
v0 = 9.3915 m/s
Since the total velocity must be 15.5, the vertical componet is:
v0 = 15.5sin(T)
and T = 37.2938 degrees
b. The horizontal velocity (call it u) is 15.5cos(T). So:
u = 12.3309 m/s
The time the ball travels is:
t = (v0/9.8) = 0.95832 seconds
distance = u*t = (12.3309)(0.95832)
distance = 11.8169 meters
c.This is the “u” from above.
Speed of ball as it reaches the target is 12.3309 m/s
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