Question

An airboat with mass 4.38 102 kg, including the passenger, has an engine that produces a net horizontal force of 8.12 102 N, after accounting for forces of resistance.

(a) Find the acceleration of the airboat. ____________m/s^2

(b) Starting from rest, how long does it take the airboat to reach a speed of 16.5 m/s?_______________s

(c) After reaching that speed, the pilot turns off the engine and drifts to a stop over a distance of 50.0 meters. Find the resistance force, assuming it's constant. __________N

(d) Suppose the pilot, starting again from rest, opens the throttle partway. At a constant acceleration, the airboat then covers a distance of 63.6 m in 12.0 s. Find the net force acting on the boat.___________ N

Answer 1

a )

using equation F = m a

a = F / m

a = 8.12 X 10² N / 4.38 X 10² kg

a = 1.853 m/sec²

the acceleration of the airboat is ____1.853____m/s²

b )

using V = u + at

16.5 = 0 + 1.853 t

t = 16.5 / 1.853

t = 8.905 sec

it take the airboat to reach a speed of 16.5 m/s is __t = 8.905___sec.

c )

using V² - u = 2 a s

0² - 16.5² = 2 X a X 50

- 16.5² = 2 X a X 50

a = - 2.7225 m/sec²

then the resistive force is F = ma

F = 438 X 2.7225

F = 1192.455 N

the resistance force is ___1192.455___N

d )

using S = u t + 1/2 a t²

63.6 = 0 + 1/2 X a X 12²

a = 63.6 / 0.5 X 12²

a = 0.8833 m/sec²

F = ma

= 438 X 0.8833

F = 386.89 N

the net force acting on the boat.__386.89 N __N