A boat moves through the water with two forces acting on it. One is a 1500 N forward push by the motor, and the other is an 1400 N resistive force due to the water.
(a) What is the acceleration of the 1100 kg boat?
m/s 2
(b) If it starts from rest, how far will it move in 7.0 s?
m
(c) What will its velocity be at the end of this time?
m/s
To find the acceleration of the boat, we need to calculate the net force acting on it. The net force is the difference between the forward push by the motor and the resistive force due to the water.
(a) Net force = Forward push - Resistive force
Net force = 1500 N - 1400 N
Net force = 100 N
Next, we can use Newton's second law of motion to find the acceleration of the boat. The formula is:
Net force = mass * acceleration
100 N = 1100 kg * acceleration
acceleration = 100 N / 1100 kg
acceleration ≈ 0.091 m/s^2
Therefore, the acceleration of the boat is approximately 0.091 m/s^2.
(b) To calculate the distance the boat will move in 7.0 seconds, we can use the kinematic equation:
distance = initial velocity * time + 0.5 * acceleration * time^2
Since the boat starts from rest, the initial velocity is 0 m/s. Plugging in the values, we get:
distance = 0 * 7.0 + 0.5 * 0.091 * (7.0)^2
distance ≈ 0.5 * 0.091 * 49
distance ≈ 2.2275 m
Therefore, the boat will move approximately 2.2275 meters in 7.0 seconds.
(c) Finally, to find the velocity of the boat at the end of this time, we can use the kinematic equation:
final velocity = initial velocity + acceleration * time
final velocity = 0 + 0.091 * 7.0
final velocity ≈ 0.637 m/s
Therefore, the velocity of the boat at the end of 7.0 seconds is approximately 0.637 m/s.
To find the acceleration of the boat, we can use Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
(a) To calculate the acceleration of the boat, we need to subtract the resistive force due to the water from the forward force by the motor:
Net force = Forward force - Resistive force
= 1500 N - 1400 N
= 100 N
Now, we can use Newton's second law:
Net force = mass × acceleration
100 N = 1100 kg × acceleration
Rearranging the equation to solve for acceleration:
acceleration = Net force / mass
acceleration = 100 N / 1100 kg
acceleration ≈ 0.091 m/s^2
Thus, the acceleration of the boat is approximately 0.091 m/s^2.
(b) To find how far the boat will move in 7.0 seconds, we can use the kinematic equation:
distance = initial velocity × time + 0.5 × acceleration × time^2
Since the boat starts from rest, the initial velocity is zero. Therefore, the equation becomes:
distance = 0.5 × acceleration × time^2
= 0.5 × 0.091 m/s^2 × (7.0 s)^2
= 0.5 × 0.091 m/s^2 × 49.0 s^2
≈ 2.23 meters
Thus, the boat will move approximately 2.23 meters in 7.0 seconds.
(c) To find the velocity of the boat at the end of 7.0 seconds, we can use another kinematic equation:
final velocity = initial velocity + acceleration × time
Since the boat starts from rest, the initial velocity is zero. Therefore, the equation becomes:
final velocity = acceleration × time
= 0.091 m/s^2 × 7.0 s
≈ 0.64 m/s
Thus, the velocity of the boat at the end of 7.0 seconds is approximately 0.64 m/s.
(a) net force = M * a
Solve for a. The net force is 100 N
(b) X = (a/2)t^2
Use the acceleration "a" from part a.
t = 7 s.
(c) V = a * t