a stone is thrown vertically downwards with a speed of 10 m/s from a bridge. acceleration under gravity (9.8 m/s squared). the stone strikes the water 1.8 s later. from what height above the water was the stone thrown? assume 2 significant digits.
To solve this problem, we can use the equation of motion for vertical motion:
s = ut + 1/2 * at^2
where:
s = height
u = initial velocity
a = acceleration
t = time
In this case, the stone is thrown downwards, so the initial velocity u is -10 m/s (negative sign indicates the downward direction), acceleration a is -9.8 m/s^2 (negative sign indicates acceleration due to gravity), and the time t is 1.8 s.
Substituting these values into the equation:
s = -10 * 1.8 + 1/2 * (-9.8) * (1.8)^2
s = -18 - 8.82
s ≈ -26.82
Since the height cannot be negative, we take the magnitude of s:
height = |-26.82| ≈ 26.82 meters.
Therefore, the stone was thrown from a height of approximately 26.82 meters above the water.
a 55kg person is skating on the Rideadu canal. she reaches a maximum speed and then glides to a stop in 100 m. the coefficient between her skates and the ice is 0.010. what is the work done by kinetic friction?
To calculate the work done by kinetic friction, we can use the formula:
Work = Force * Distance
The force of kinetic friction can be calculated using the equation:
Force of Kinetic Friction = coefficient of friction * Normal Force
The normal force is equal to the weight of the person, which can be calculated as:
Weight = mass * acceleration due to gravity
Given:
Mass (m) = 55 kg
Coefficient of friction (μ) = 0.010
Distance (d) = 100 m
Acceleration due to gravity (g) = 9.8 m/s^2
First, calculate the weight:
Weight = mass * acceleration due to gravity
Weight = 55 kg * 9.8 m/s^2
Weight = 539 N
Next, calculate the force of kinetic friction:
Force of Kinetic Friction = coefficient of friction * Normal Force
Force of Kinetic Friction = 0.010 * 539 N
Force of Kinetic Friction = 5.39 N
Finally, calculate the work done:
Work = Force * Distance
Work = 5.39 N * 100 m
Work = 539 J
Therefore, the work done by kinetic friction is 539 Joules.
To find the height from which the stone was thrown, we can use the equations of motion. Let's break the problem down into steps:
Step 1: Determine the time it takes for the stone to reach the water.
Given:
Initial velocity (u) = 10 m/s (thrown vertically downwards)
Acceleration due to gravity (a) = 9.8 m/s^2
Time (t) = 1.8 s
Using the equation of motion:
t = (v - u) / a
Rearranging the equation to solve for final velocity (v):
v = u + at
Substituting the given values:
v = 10 m/s + (9.8 m/s^2)(1.8 s)
v = 10 m/s + 17.64 m/s
v ≈ 27.6 m/s
Step 2: Calculate the height from which the stone was thrown.
We can use the equation of motion:
v^2 = u^2 + 2as
Solving for the height (s):
s = (v^2 - u^2) / (2a)
Substituting the values:
s = (27.6 m/s)^2 - (10 m/s)^2 / (2 * 9.8 m/s^2)
s = 761.76 m^2/s^2 - 100 m^2/s^2 / 19.6 m/s^2
s = 661.76 m^2/s^2 / 19.6 m/s^2
s ≈ 33.8 m
Therefore, the stone was thrown from approximately 33.8 meters above the water.