A rock is thrown upward at an initial velocity of 42 ft/sec from a platform 28 ft?

Question

A rock is thrown upward at an initial velocity of 42 ft/sec from a platform 28 ft high. How many seconds will it take to hit ground? (Round to 2 decimal places.)

Answer 1

For these types of equation, the formula is:

S = ‒½ g t² + V₀t + S₀

where S is the height of the object at a certain time t.
g is the gravitational acceleration (g is about 32 ft/s² or 9.8m/s²)
V₀ is the initial velocity and S₀ is the initial height.

In this case,
S(t) = -16t² + 42t + 28 ... get its zero.
-16t² + 42t + 28 = 0 ......... 8t² - 21t - 14 = 0

t = [21 + √(441 + 448)]/16 = 3.18 seconds.
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Answer 2

v = v0 + gt
v0 = initial velocity = 42 ft/sec
g = acceleration of gravity = -32 ft/sec^2

At the peak v=0 = 42 - 32t
t at peak = 42/32 = 21/16 seconds = 1.3125 seconds
Distance upward = D= v0t + (1/2)gt^2
D = 42(42/32) + 16(42/32)^2
D = 27.5625 feet

It now falls to the ground. s = (1/2)gt^2
s = 28 + 27.5625 = 55.5625 feet = 16t^2
t^2 = SQRT(55.5625/16)
t = 1.8635 seconds

It takes 1.3125 seconds for the rock to reach the hightest point
It then takes it 1.8635 seconds to drop to the ground

Total time in air = 3.176 seconds= 3.18 seconds

Answer 3

This is a projectile problem, We assume that the rock is projected vertically upwards with v0=v(0)= 42 ft/s

v^2 - v0^2 = (1/2)a t^2 = - (1/2)g t^2
at highest point v= 0,
so time to get to the highest point:
0 - v0^2 = - (1/2) 32.2 t^2
t^2 = v0^2/16.1 = 42^2/16.1 = 109.57
t = 10.47
the rock takes the same time to get down to platform level
(h = 28ft) with the same velocity down: 42ft/sec

Now Use the conservation of energy principle.
at platform, Kinetic energy, KE = 1/2 m v^2 = (m/2)42^2
potential energy = mgh = m (32.2)(28)
Let final velocity at ground (h=0) = (m/2)v^2
then
(m/2)v^2 = (m/2)42^2 + m(32.2)(28)
v^2 = 42^2 + 64.4(28) = 3567.2
v = 59.73
so time to go down 28 ft is from:
59.73^2 - 42^2 = (1/2)(32.2)t^2
64.4(28) = (1/2)(32.2)t^2
t^2 = 112
t = 10.58

total time = 10.47 + 10.47 + 10.58 = 31.5 sec
The 1st term is the time to go from platform to highest point, 2nd term is the same time down to platform level,
3rd time is the time from platform to ground level (down 28ft)

Answer 4

Do the problem yourself. Yahoo answers isn't a place where you can cheat on your homework. Plus, you need the volume of the rock.