Question

A boat is drifting with a speed of 5.0\,\dfrac{\text m}{\text s}5.0 s m ​ 5, point, 0, space, start fraction, m, divided by, s, end fraction to the right when the driver turns on the motor. The boat speeds up for 6.0\,\text s6.0s6, point, 0, space, s with an acceleration of 4.0\,\dfrac{\text m}{\text s^2}4.0 s 2 m ​ 4, point, 0, space, start fraction, m, divided by, s, start superscript, 2, end superscript, end fraction leftward. What is the displacement of the boat over the 6.0\,\text s6.0s6, point, 0, space, s time interval?

Answer 1

Answer:

$d=42m(-\hat{i})$

Explanation:

For this problem, we need to apply the formulas of constant accelerated motion.

To obtain the boat displacement we need to calculate the displacement because of the river flow and the displacement done because of the boat motor.

for the river:

$d_r=v*t\\d_r=5m/s*6s\\d_r=30m(\hat{i})$

for the boat:

$x=\frac{1}{2}*a*t^2\\\\x=\frac{1}{2}*4.0m/s*(6s)^2\\\\\\x=72m(-\hat{i})$

So the final displacement is given by:

$d=dr+x\\d=30m-72m\\d=42m(-\hat{i})$

Answer 2

Answer: -42

Explanation: