Ben threw a ball up in the air with an initial velocity of 15m/s from a 17m high platform.
A.What is the max height reached before failling down?
B.How long was the ball in the air?
C.What is the final velocity of the ball upon reaching the ground?
v =vi - 9.81 t
at top
0 = 15 - 0.981 t
t = 15/9.81 = 1.53 seconds rising
h = 17 + 15(1.53) -4.9(1.53)^2
= 17 + 22.9 - 11.5 = 28.5 meters maxh
how long to fall from there and fast does it hit?
0 = 28.5 - 4.9 t^2
t falling = 5.81 seconds
so totsl time = 5.81+1.53 = 7.34 s
how fast at crash?
v = 0 -9.81(5.81) = - 57 meters/s
A. The equation for this would be:
h(t)=-4.9t²+15t+17
The ball will reach its maximum height at -b/2a, where b and a come from the standard equation y=ax²+bx+c. So:
-15/-9.8 is about 1.5 seconds
The height would be :
h=-4.9(1.5)²+15(1.5)+17=28.475 m
B. If h(t)=0, then
-4.9t²+15t+17=0
4.9t²-15t-17=0
using the quadratic formula, we get a positive value for t of 3.94 secs
C. 3.94-1.5=2.44 seconds in free fall.
V=9.8 m/s² x 2.44 seconds=23.912 m/s
☺☺☺☺
In the time of falling, should it be square rooted? Since there is t^2 left
To answer these questions, we can use some basic equations of motion.
A. To find the maximum height reached by the ball before falling down, we need to use the equation for vertical displacement. The equation is:
h = (v_i^2)/(2g) + h_i
where:
h = maximum height reached
v_i = initial velocity of the ball
g = acceleration due to gravity (approximately 9.8 m/s^2)
h_i = initial height of the ball
Using the given values, we can substitute them into the equation to find the maximum height reached:
h = (15^2)/(2 * 9.8) + 17
h ≈ 11.79 + 17
h ≈ 28.79 m
So, the maximum height reached by the ball before falling down is approximately 28.79 meters.
B. To find the time the ball was in the air, we can use the equation for time of flight:
t = 2 * v_i / g
Using the given values, we can substitute them into the equation to find the time of flight:
t = 2 * 15 / 9.8
t ≈ 3.06 s
So, the ball was in the air for approximately 3.06 seconds.
C. To find the final velocity of the ball upon reaching the ground, we can use the equation for final velocity:
v_f = v_i + g * t
Using the given values, we can substitute them into the equation to find the final velocity:
v_f = 15 + 9.8 * 3.06
v_f ≈ 44.988 m/s
So, the final velocity of the ball upon reaching the ground is approximately 44.988 meters per second.