When the ball starts its motion from the ground, its potential energy is zero, so all its mechanical energy is kinetic energy of the motion:
where m is the ball's mass and v its initial velocity, 20 m/s.
When the ball reaches its maximum height, h, its velocity is zero, so its mechanical energy is just gravitational potential energy:
for the law of conservation of energy, the initial mechanical energy must be equal to the final mechanical energy, so we have
From which we find the maximum height of the ball:
Therefore, the answer is
yes, the ball will reach the top of the tree.
Answer:
m = 0.4 [kg]
Explanation:
Weight is considered as a force and this is equal to the product of mass by gravitational acceleration.
where:
W = weight = 0.8 [N]
m = mass [kg]
g = gravity acceleration 2[N/kg]
Therefore:
Answer:
The railroad tracks are 13 m above the windshield (12 m without intermediate rounding).
Explanation:
First, let´s calculate the time it took the driver to travel the 27 m to the point of impact.
The equation for the position of the car is:
x = v · t
Where
x = position at time t
v = velocity
t = time
x = v · t
27 m = 17 m/s · t
27 m / 17 m/s = t
t = 1.6 s
Now let´s calculate the distance traveled by the bolt in that time. Let´s place the origin of the frame of reference at the height of the windshield:
The position of the bolt will be:
y = y0 + 1/2 · g · t²
Where
y = height of the bolt at time t
y0 = initial height of the bolt
g = acceleration due to gravity
t = time
Since the origin of the frame of reference is located at the windshield, at time 1.6 s the height of the bolt will be 0 m (impact on the windshield). Then, we can calculate the initial height of the bolt which is the height of the railroad tracks above the windshield:
y = y0 + 1/2 · g · t²
0 = y0 -1/2 · 9.8 m/s² · (1.6 s)²
y0 = 13 m
Answer:
Explanation:
Given
Radioactive material is found to decrease 40% of its original value in
Sample at any time is given by
where,
Put values
Taking natural logarithm both side