A body is thrown vertically upward from the ground with an initial velocity of 96 ft/sec. Find the maximum height attain by the body
s-maximum height attained by the body in feet
Vo-initial velocity(ft|sec)
t-time(sec)
s=96t-16t^2
16t^2=96t
16t^2/16=96t/16
t^2=6t
t^2-6t=0
t^2-6t+9=0
(t-3)(t-3)=0
t=3 sec.
s=96t-16t^2
s=96(3)-16(3)^2
s=288-144
s=144 feet
v = Vi - 32 t
0 = 96 - 32 t
t = 3 s
h = Vi t - 16 t^2
h = 96(3) - 16(3)^2
h = 288 - 144 = 144 ft
Well, if the body was thrown with that much speed, I bet it reached some pretty dazzling heights. I'm picturing it touching the clouds and waving at the birds. But let's do some math to find out the exact height!
To find the maximum height, we need to use some good ol' physics equations. The formula we need is h = (v^2) / (2g), where h represents the maximum height, v is the initial velocity, and g is the acceleration due to gravity.
In this case, the initial velocity (v) is 96 ft/sec. And since we're on Earth, we'll use the acceleration due to gravity (g) as 32 ft/sec^2.
So, plugging in these values into our formula, we get:
h = (96^2) / (2 * 32) = 9216 / 64 = 144 ft
Hooray! The body reached a maximum height of 144 feet. That's pretty high up! Just make sure to catch it on its way down, or it might make a not so graceful landing.
To find the maximum height attained by the body, you can use the formula for the time it takes for an object to reach its maximum height and then use that time to find the height.
Step 1: Find the time it takes to reach maximum height.
Using the equation for vertical motion under constant acceleration, we have:
Vf = Vi + at
where Vf is the final velocity, Vi is the initial velocity, a is the acceleration, and t is the time.
Since the body is thrown upwards, the final velocity at the maximum height is 0 ft/sec, the initial velocity Vi is 96 ft/sec, and the acceleration due to gravity a is -32 ft/sec^2 (taking downward direction as negative).
Plugging in the values, we have:
0 = 96 + (-32)t
-96 = -32t
Dividing both sides by -32, we get:
t = 3 seconds
Step 2: Find the maximum height.
Using the equation for vertical motion under constant acceleration, we have:
d = Vit + 0.5at^2
where d is the displacement (height), Vi is the initial velocity, a is the acceleration, and t is the time.
Plugging in the values, we have:
d = (96)(3) + 0.5(-32)(3)^2
d = 288 - 144
d = 144 ft
Therefore, the maximum height attained by the body is 144 ft.
To find the maximum height attained by the body, we can use the equations of motion.
The equation that relates the initial velocity (u), final velocity (v), acceleration (a), and displacement (s) is given by:
v^2 = u^2 + 2as
Since the body is thrown vertically upward, the initial velocity (u) is 96 ft/sec. The final velocity (v) at the maximum height is 0 ft/sec because at the highest point, the body momentarily comes to rest before falling back down. The acceleration (a) due to gravity is -32 ft/sec^2 (taking downward direction as negative).
Substituting the known values into the equation:
0^2 = 96^2 + 2(-32)s
0 = 9216 - 64s
64s = 9216
s = 9216 / 64
s ≈ 144 ft
Therefore, the maximum height attained by the body is approximately 144 feet.