A boat moves through the water with two
forces acting on it. One is a 2.80×10
3
N
forward push by the motor, and the other is a
1.56×10
3
N resistive force due to the water.
a)What is the acceleration of the 1312.6 kg
boat?
Answer in units of m/s^2
b)If it starts from rest, how far will it move in
17.2 s?
Answer in units of m
c)What will be its speed at the end of this time
interval?
Answer in units of m/s
a) To find the acceleration of the boat, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration.
Given:
Force forward push (F1) = 2.80 × 10^3 N
Resistive force (F2) = 1.56 × 10^3 N
Mass of the boat (m) = 1312.6 kg
The net force acting on the boat is the difference between the forward push and the resistive force:
Net force (Fnet) = F1 - F2
Substituting the given values, we have:
Fnet = 2.80 × 10^3 N - 1.56 × 10^3 N
Now we can use Newton's second law to calculate the acceleration:
Fnet = m × a
Substituting the values, we have:
2.80 × 10^3 N - 1.56 × 10^3 N = 1312.6 kg × a
Simplifying the equation:
1.24 × 10^3 N = 1312.6 kg × a
Now solve for acceleration:
a = (1.24 × 10^3 N) / (1312.6 kg)
a ≈ 0.944 m/s^2
Therefore, the acceleration of the boat is approximately 0.944 m/s^2.
b) To find the distance the boat will move in 17.2 seconds, we can use the equation of motion:
Distance (d) = initial velocity (u) × time (t) + 0.5 × acceleration (a) × time^2
Since the boat starts from rest, the initial velocity (u) is 0 m/s.
Substituting the values, we have:
d = 0 × 17.2 s + 0.5 × 0.944 m/s^2 × (17.2 s)^2
Simplifying the equation:
d = 0 + 0.5 × 0.944 m/s^2 × (296.84 s^2)
Calculating the distance:
d = 0 + 0.5 × 0.944 m/s^2 × 525.6768 s^2
d ≈ 249.03 m
Therefore, the boat will move approximately 249.03 meters in 17.2 seconds.
c) To find the speed of the boat at the end of the 17.2-second time interval, we can use the equation of motion:
Final velocity (v) = initial velocity (u) + acceleration (a) × time (t)
Since the boat starts from rest, the initial velocity (u) is 0 m/s.
Substituting the values, we have:
v = 0 + 0.944 m/s^2 × 17.2 s
Calculating the speed:
v = 0 + 0.944 m/s^2 × 17.2 s
v ≈ 16.25 m/s
Therefore, the speed of the boat at the end of the 17.2-second time interval is approximately 16.25 m/s.