The accelerating force of the wind on a small 250-kg sailboat is 707 N northeast. If the drag of the keel is 500 N acting west, what is the acceleration of the boat?Select one:a.1.5 m/s2 due eastb.2.5 m/s2 due northc.2.0 m/s2 due northd.3.0 m/s2 northeast
Question
The accelerating force of the wind on a small 250-kg sailboat is 707 N northeast. If the drag of the keel is 500 N acting west, what is the acceleration of the boat?Select one:a.1.5 m/s2 due eastb.2.5 m/s2 due northc.2.0 m/s2 due northd.3.0 m/s2 northeast
Solution
First, we need to resolve the force of the wind into its components. The wind is acting 707 N northeast, which means it has equal components to the north and to the east. So, the force of the wind to the north (Fn) and to the east (Fe) is 707/sqrt(2) = 500 N.
The net force acting on the boat to the east (Fe_net) is just the force of the wind to the east, which is 500 N. The net force acting on the boat to the north (Fn_net) is the force of the wind to the north minus the drag of the keel, which is 500 - 500 = 0 N.
The acceleration of the boat to the east (ae) is the net force to the east divided by the mass of the boat, which is 500/250 = 2 m/s^2. The acceleration of the boat to the north (an) is the net force to the north divided by the mass of the boat, which is 0/250 = 0 m/s^2.
So, the acceleration of the boat is 2 m/s^2 to the east and 0 m/s^2 to the north. This means the correct answer is a. 1.5 m/s^2 due east.
Similar Questions
A 2000-kg sailboat experiences an eastward force of 2000 N by the ocean tide and a wind force against its sails with magnitude of 6000 N directed toward the northwest (45° N of W). What is the direction of the resultant acceleration?Select one:a.62° N of Wb.30° N of Ec.60° N of Ed.74° N of W
A model sailboat is slowly sailing west across a pond at 0.310 m/s. A gust of wind blowing at 28.3° south of west gives the sailboat a constant acceleration of magnitude 0.314 m/s2 during a time interval of 2.18 s. If the net force on the sailboat during the 2.18-s interval has magnitude 0.318 N, what is the sailboat's mass? What is the new velocity of the boat after the 2.18 s gust of wind? And what is the new direction of the boat after the 2.18 s gust of wind?
A boat moves with a velocity of 17.3 m/s, N in a river which flows with a velocity of 7.33 m/s, west. Calculate the boat's resultant velocity with respect to due north.
An airplane of mass 1.2 × 104 kg tows a glider of mass 0.6 × 104 kg. The airplane propellers provide a net forward thrust of 5.4 × 104 N. What is the glider's acceleration?Select one:a.9.8 m/s2b.6.0 m/s2c.2.0 m/s2d.3.0 m/s2
Identify which of the following quantities are accelerations. 17 km/h120 m/s/s upwards0.2 m/s/s southwest7 m/s to the right5.3 m/s/s
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.