What is the maximum height of the ball? What time will the maximum height be attained?

Question

Suppose you throw a baseball straight up at a velocity of 64 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. This function is s = -16t2 + v0t + s0
•16 represents 1/2g, the gravitational pull due to gravity (measured in feet per second2).
•v0 is the initial velocity (how hard do you throw the object, measured in feet per second).
•s0 is the initial distance above ground (in feet). If you are standing on the ground, then s0 = 0

Answer 1

The miximum height reached by the ball is when the velocity of the ball is zero. Since the initial velocity is 64ft/s, the distance above the ground equation becomes s = -16t^2 + 64t + 0
s = -16t^2 + 64t . Taking derivaties to find velocity equation.
ds/dt = -32t +64. At maximum height ds/dt = 0.
Thus, -32t + 64 = 0
32t = 64
t = 2
So, maximum height is reached at t = 2s. So the maximum height reached by the ball:
s = -16(2)^2 + 64*2
s = -64 +128
s = 64 feet.
The maximum height reached by the ball is 64 feet.

Answer 2

... the maximum height happens when the upward direction stops and the ball begins to fall. (when v=0)

since we started with v0=64, let's consider when the velocity (call it "vg") due to gravity equals -64.

since velocity = acc x time
vg = 32 t
64 = 32 t
t = 2
=> maximium height will be attained after 2 seconds.
(answer 2)

max height:
s = -16 t^2 + v0t + s0
s= -16x(2^2) + (64x2 + s0
= -64 + 128 + s0
= 64 + s0 ........ max height
(answer 1)

if s0 = 0, then maxheight = 64 feet (above ground)

Answer 3

well, you know that gravity is pulling on the ball, so that it is decelerating at 32 ft/s^2. Therefore after 1 second, it will be going 64-32=32 ft/sec upward. After 2 seconds it will be going 32-32=0ft/sec upward. What does this mean?

Answer 4

using V=Vo + A(t), you reach your highest point (where V=0) at 2 seconds. so another equation for linear acceleration is: x (displacement) = Vo(t)+1/2A(t^2)

so x = 64 f/s (2s) + (1/2) (-32.2 f/s^2) (2^2)

=63.6 ft

Answer 5

there is a purpose why teachers give you homework. the purpose is not to learn how to use yahoo answers.