A ball is thrown vertically upward with an initial velocity of 64 feet per second. The distance(in feet) of the ball from the ground after t seconds is s=64t-16t.
At what time will the ball strike the ground?
For what time t is the ball more than 28 feet above the ground.
The ball will strike the ground when t is _____ seconds.
The ball is more than 28 feet above the ground for the time t when ____<t<____.
you should proably first simplify 64t-16t = 48t. Then, 48t=s. Plug it in, see what you get.
s = 64t - 16t^2
s=0 at t= 0,2
ball is more than 28 ft high when
64t - 16t^2 > 28
-16t^2 + 64t - 28 > 0
-4(2t-1)(2t-7) > 0
1/2 < t < 7/2
To find the time at which the ball strikes the ground, we need to set the equation s = 0, where s represents the distance from the ground.
So, we have:
0 = 64t - 16t
Combining like terms:
0 = 48t
To solve for t, we divide both sides by 48:
0/48 = t
Therefore, the ball will strike the ground when t is 0 seconds.
To find the time at which the ball is more than 28 feet above the ground, we need to set the equation s > 28.
So, we have:
64t - 16t > 28
Combining like terms:
48t > 28
Dividing both sides by 48:
t > 28/48
Simplifying:
t > 7/12
Therefore, the ball is more than 28 feet above the ground for the time t when 7/12 < t.
To find the time when the ball strikes the ground, we need to find the value of t when the distance of the ball from the ground is zero.
Given: s = 64t - 16t
Setting s equal to zero, we have:
0 = 64t - 16t
Combining like terms:
0 = 48t
Dividing both sides by 48:
0 = t
Hence, the ball will strike the ground when t is 0 seconds.
To find the time when the ball is more than 28 feet above the ground, we need to find the values of t when the distance, s, is greater than 28.
Given: s = 64t - 16t
Setting s greater than 28:
28 < 64t - 16t
Combining like terms:
28 < 48t
Dividing both sides by 48:
28/48 < t
Simplifying:
7/12 < t
So, the ball is more than 28 feet above the ground for the time t when t is greater than 7/12 seconds.
Putting it together:
1. The ball will strike the ground when t is 0 seconds.
2. The ball is more than 28 feet above the ground for the time t when 7/12 < t.