Physics MCAT Question?

Question

An airplane is susceptible to substantial deflection off course due to wind. A pilot calls the engines' contribution the airspeed. This motion relative to the air, combined with the wind velocity, results in the ground speed, or velocity relative to fixed terrestrial objects.

When a parachutist typically leaves an airplane, it is not so much a jump as a drop. He steps out of a door or lets go of a strut under the wing, not giving him any significant velocity relative to the airplane. He becomes subject to gravity without the lift of the wings. Air resistance allows the plane to get ahead of him. If we neglect this drag effect, then the parachutist's constant horizontal velocity and constant vertical acceleration gives him a trajectory resembling half of an inverted parabola. This is a reasonable assumption for the freefall before the parachute is engaged.

 

Question 1: A pilot wanting to travel northeast in a wind blowing from the west at a speed similar to her airspeed should direct her airplane in which direction? 

North? South? East? or WEST?

 

Question 2: An airplane capable of an airspeed of 100 km/hr is 60 km off the coast above the sea. If the wind is blowing from the coast out to sea at 40 km/hr, what is the least amount of time it will take for the plane to get to shore?

100 minutes? 26 Minutees? 60 minutes? or 36 minutes?

 

Question 3: Neglecting air resistance, what is the total velocity of a parachutist just before engaging his parachute, 8 s after dropping from an airplane flying horizontally at 60 m/s?

80 m/s? 140 m/s? 100 m/s? or 60 m/s?

 

Question 4: Relative to the typical dropping parachutist, one who thrusts himself downward on exiting the airplane will have:

the same acceleration and the same velocity just before engaging his paracute

lower acceleration but the same velocity just before engaging his parachute.

the same acceleration but greater velocity just before engaging his parachute.

greater acceleration and greater velocity just before engaging his parachute.

 

Answer 1

(3)

Step 1:

Parachutist is freely jumping from the plane, so he is treated as a freely falling body.

Vertical downward velocity :

Freely falling bodies have a downward velocity is .

Here, is acceleration due to gravity (10 m/s² ) and t  is time.

Velocity after 8 seconds :

Airplane flying vertically at speed of 80 m/s.

Step 2:

Find the resultant velocity.

Resultant velocity is the vector sum of horizontal and vertical velocities of parachutist.

Therefore, the resultant velocity is 100 m/s.

Option (c) is correct choice.

Solution :

 Option (c) is correct choice.

Answer 2

(4)

Parachutist is freely jumping from the plane, so he is treated as a freely falling body.

Acceleration of Freely falling bodies :

Acceleration of a freely-falling object is constant - that is, the object's acceleration does not change while the object is in free fall.

The acceleration of a freely-falling object near the surface of the Earth is about 9.8 m/s².

Velocity of Freely falling bodies :

The acceleration of a freely-falling object is constant means that the velocity of a freely-falling object changes at a constant rate.

So the freely falling bodies has a greater final velocities.

Therefore, parachutist have same acceleration but greater velocity just before engaging his parachute.

Option (c) is correct choice.

Answer 3

(1)

A pilot wants to travel northeast direction.

Wind is blowing from the west.

Therefore, direction of wind speed is towards east.

Triangle law of vectors addition:

If the two vectors represented by the two adjacent sides of triangle, then the third side of the triangle determines the addition of the two vectors as shown.

Wind speed is towards east direction.

The airplane should move in the north-east direction.

If the airspeed is in north direction, then the resultant component of north and east gives northeast direction.

Hence the airspeed should direct in north direction so that airplane moves in the north-east direction.

Therefore, airspeed is in north direction.

Option (a) is correct.

Answer 4

2)
Airspeed of airplane is kmph.

Wind is blowing from the coast out to sea at kmph.

Wind is blowing from the coast out to sea means that it opposes the airspeed.

Therefore, resultant relative speed of airplane is kmph.

Airplane is km off the coast above the sea.

Distance traveled by the plane to reach the shore is km.

  

.

Substitute km and kmph in the expression.

 hr.

.

Therefore, time taken by the plane to reach the shore is .

Option (c) is correct.