The acceleration due to gravity near the surface of Mars is 3.72ms^-2 . A
rock is thrown straight up from the surface with an initial velocity
of 23ms^-2 . How high does it go?
a = -3.72
v = -3.72t + c
when t = 0, v = 23
so c = 23
v = -3.72t + 23
s = -1.86t^2 + 23t + k , where s is the height
when t = 0 , s = 0, so k = 0
max of s is obtained when v = 0
3.72t = 23
t = 23/3.72 = 2300/372 = 575/93
when t = 575/93
s = .... use your calculator
I got appr 71.1 m
check my above arithmetic
To find the height the rock reaches, we can use the kinematic equation:
vf^2 = vi^2 + 2as
Where:
vf = final velocity (0 m/s at the highest point)
vi = initial velocity (23 m/s)
a = acceleration due to gravity on Mars (3.72 m/s^2)
s = height or displacement
Rearranging the equation, we have:
s = (vf^2 - vi^2) / (2a)
Since the rock stops at the highest point, the final velocity at that point is 0 m/s. Plugging in the values:
s = (0^2 - 23^2) / (2 * -3.72)
s = (-529) / (-7.44)
s = 71.07 meters
Therefore, the rock reaches a height of approximately 71.07 meters.
To calculate the height the rock reaches, we can use the equations of motion.
The first equation of motion is:
v = u + at
Where:
v is the final velocity (which will be zero at the highest point),
u is the initial velocity,
a is the acceleration, and
t is the time taken.
In the case of the rock thrown straight up, the final velocity is zero at the highest point, the initial velocity is 23 m/s, and the acceleration is -3.72 m/s² (negative because the acceleration due to gravity opposes the motion). Plugging these values into the equation, we get:
0 = 23 - 3.72t
Solving for t:
3.72t = 23
t = 23 / 3.72
t ≈ 6.18 seconds
Now, we can use the second equation of motion to calculate the maximum height the rock reaches. The equation is:
s = ut + 0.5at²
Where:
s is the displacement (height),
u is the initial velocity,
t is the time taken, and
a is the acceleration.
Plugging in the values, we get:
s = (23 × 6.18) + 0.5 × (-3.72) × (6.18)²
s ≈ 142.52 meters
Therefore, the rock reaches a height of approximately 142.52 meters.