A stone is thrown vertically upwards from the top of a tower 50.0m high with an intial velocity of 20.0m/s. (a) whats the maximum height the stone reaches? (b) Whats the time it takes to reach the maximim height? (c) What is the total distance it covers?
Initial velocity=20 m/s
Final velocity=0m/s
Height using third equation of motion 2as=v²-u²
Acceleration due to gravity = -9.8 m/s(-10m/s)
- sign for acceleration in opposite direction
2*-10*s=0²-20²
-20s=-400
S=-400/-20=20metres
So maximum height= height of tower + height of stone from tower
50+20=70 m
b) time taken using first equation of motion v=u+at
0=20+(-10t)
-20=-10t
t=-20/-10 =2 seconds
vf^2=2gh where h is the height from the tower. for total height, add 50m
time? h=hi+vi*t-4.9t^2
solve for t
distance? 2h+50
To answer these questions, we can use the equations of motion. Let's break down each question and solve them step by step:
(a) What's the maximum height the stone reaches?
We can use the kinematic equation for displacement to find the maximum height. The equation is:
h = (v^2 - u^2) / (2g)
Given:
Initial velocity (u) = 20.0 m/s
Acceleration due to gravity (g) = 9.8 m/s^2
Using these values in the equation:
h = (0^2 - 20^2) / (2 * -9.8)
h = (-400) / (-19.6)
h = 20.41 m
Therefore, the maximum height the stone reaches is approximately 20.41 m.
(b) What's the time it takes to reach the maximum height?
To find the time, we can use the kinematic equation for vertical velocity. The equation is:
v = u + gt
Given:
Initial velocity (u) = 20.0 m/s
Acceleration due to gravity (g) = 9.8 m/s^2
Vertical velocity at maximum height (v) = 0 m/s (at the top)
Using these values in the equation:
0 = 20 + (-9.8)t
-20 = -9.8t
t = -20 / -9.8
t ≈ 2.04 s
Therefore, it takes approximately 2.04 seconds to reach the maximum height.
(c) What's the total distance it covers?
The total distance covered by the stone will be the sum of the upward displacement and the downward displacement.
Upward displacement = maximum height reached = 20.41 m
Downward displacement = height of the tower = 50.0 m
Total distance covered = Upward displacement + Downward displacement
Total distance covered = 20.41 m + 50.0 m
Total distance covered = 70.41 m
Therefore, the total distance covered by the stone is approximately 70.41 m.
To solve this problem, we can use the equations of motion. Let's break it down step by step:
(a) To find the maximum height the stone reaches, we need to determine the highest point it reaches during its motion. We can use the equation of motion:
v^2 = u^2 + 2as
Where:
v = final velocity (which is 0 since at the maximum height the stone momentarily stops before falling back down)
u = initial velocity (20.0m/s)
a = acceleration (which is acceleration due to gravity, -9.8m/s^2)
s = displacement, which is the maximum height we want to find
Rearranging the equation, we get:
s = (v^2 - u^2) / (2a)
Substituting the known values, we have:
s = (0^2 - 20.0^2) / (2 * -9.8)
s = 400 / -19.6
s = -20.41m
Since the displacement cannot be negative in this case, we take the magnitude of the value:
Maximum height = |s| = 20.41m
Therefore, the maximum height the stone reaches is approximately 20.41 meters.
(b) To find the time it takes to reach the maximum height, we can use the equation of motion:
v = u + at
At the maximum height, the final velocity (v) is 0, and the acceleration (a) is -9.8m/s^2. The initial velocity (u) is 20.0m/s. Solving for time (t):
0 = 20.0 + (-9.8)t
9.8t = 20.0
t = 20.0 / 9.8
t = 2.04s
Therefore, it takes approximately 2.04 seconds for the stone to reach the maximum height.
(c) To find the total distance covered, we need to consider the distance traveled upwards and downwards. The stone covers the same distance on its way down as it does on its way up.
So, the total distance traveled is the distance covered upwards plus the distance covered downwards.
Distance covered upwards = maximum height = 20.41m
Distance covered downwards = maximum height = 20.41m
Total distance = Distance covered upwards + Distance covered downwards = 20.41m + 20.41m = 40.82m
Therefore, the total distance covered by the stone is approximately 40.82 meters.