Answer:
a) The coin´s maximum height is 9.79 m above the ground.
b) The coin is 2.17 s in the air.
c) The speed is 13.82 m/s when the coin hits the ground
Step-by-step explanation:
The equations for the position and velocity of the coin are the following:
y = y0 + v0 · t + 1/2 · g · t²
v = v0 + g · t
Where
y = height at time t
y0 = initial height
v0 = initial velocity
t = time
g = acceleration due to gravity
v = velocity at time t
a) At its max-height, the velocity of the coin is 0. Using the equation of velocity, we can obtain the time at which the velocity is 0.
v = v0 + g · t
0 = 7.4 m/s - 9.8 m/s² · t
- 7.4 m/s / - 9.8 m/s² = t
t = 0.76 s
Now calculating the height of the coin at t = 0.76 s, we will obtain the maximum height:
y = y0 + v0 · t + 1/2 · g · t²
y = 0 m + 7.4 m/s · 0.76 s - 1/2 · 9.8 m/s² · (0.76 s)²
y = 2.79 m
The coin´s maximum height above the ground is 7 m + 2.79 m = 9.79 m
b) After the coin reaches its maximum height, it falls to the ground. The initial position will be the max-height (2.8 m) and the final position is the ground (-7 m). The initial velocity, v0, will be 0, because the coin is at the max-height. Then, using the equation of position we can calculate the time the coin is falling:
y = y0 + v0 · t + 1/2 · g · t²
-7 m = 2.79 m - 1/2 · 9.8 m/s² · t²
-2 ·(-7 m - 2.79 m)/ 9.8 m/s² = t²
t = 1.41 s
The coin is (1.41 s + 0.76 s) 2.17 s in the air
c) Using the equation of velocity, we can calculate the speed at time 1.41 s, when the coin hits the ground.
v = v0 + g · t
v = 0 m/s - 9.8 m/s² · (1.41 s)
v = -13.82 m/s
The speed is 13.82 m/s when the coin hits the ground.