In physics it is shown that the height "s" of a ball thrown straight up with an speed of 96 ft/sec from ground level is
s=s(t)=-16t^2 + 96t
where r is elapsed time that the ball is in the air.
a. when does the ball strike the ground? that is how long is the ball in the air?
b. what is the average speed of the ball between t=0 and t=2?
c. what is the instantaneous speed of the ball at time t?
d. what is the instantaneous speed of the ball at t=2?
e. when is the instantaneous speed of the ball equal to zero?
f. how high is the ball when its instantaneous speed equal to zero?
e. what is the instantaneous speed of the ball when it strikes the ground?
s=s(t)=-16t^2 + 96t
where r is elapsed time that the ball is in the air.
a. when does the ball strike the ground? that is how long is the ball in the air?
b. what is the average speed of the ball between t=0 and t=2?
c. what is the instantaneous speed of the ball at time t?
d. what is the instantaneous speed of the ball at t=2?
e. when is the instantaneous speed of the ball equal to zero?
f. how high is the ball when its instantaneous speed equal to zero?
e. what is the instantaneous speed of the ball when it strikes the ground?
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a) The ball is at ground level when s = 0
=> 0 = 96t - 16t²
=> 0 = 16t(6 - t)
i.e. after 6 seconds
b) after 2 seconds s = 128 feet
average speed is 128/2 = 64 ft/sec
c) v(t) => v = ds/dt = 96 - 32t
d) v(2) = 96 - 32(2) = 32 ft/sec
e) v = 0 when t = 3 seconds
f) s(3) = -16(3)² + 96(3) = -144 + 288 = 144 feet
e) v(6) = 96 - 32(6) = 96 - 192 = -96.....i.e. 96 feet/sec downwards
:)>
=> 0 = 96t - 16t²
=> 0 = 16t(6 - t)
i.e. after 6 seconds
b) after 2 seconds s = 128 feet
average speed is 128/2 = 64 ft/sec
c) v(t) => v = ds/dt = 96 - 32t
d) v(2) = 96 - 32(2) = 32 ft/sec
e) v = 0 when t = 3 seconds
f) s(3) = -16(3)² + 96(3) = -144 + 288 = 144 feet
e) v(6) = 96 - 32(6) = 96 - 192 = -96.....i.e. 96 feet/sec downwards
:)>