Question

question 7
a jet moving at 500.0 km/h due east is in a region where the wind is moving at 120.0 km/h in a direction 30.00° north of east. what is the speed of the aircraft relative to the ground?
606.9 km/h
588.7 km/h
620.2 km/h
511.3 km/h
question 8
the following questions refer to the following situation.
in a circus parade, a clown standing on a float moving at a constant forward speed drops a fake dumbbell. a child in the bleachers on the sidewalk observes the dumbbell. ignore air resistance.
the dumbbells motion as described by an acrobat walking in the parade is very similar to the clowns description of the dumbbells motion.
what do you know about the motion of the acrobat?
the acrobat is at rest with respect to the clown.
both a and b
the acrobat is at rest with respect to the float.
neither a nor b
question 9
a passenger on a bus moving east sees a man standing on a curb. from the passengers perspective, the man appears to

Explanation:

Step1: Resolve wind - velocity components

The wind has a velocity of $v_w = 120.0$ km/h at an angle $\theta=30.0^{\circ}$ north of east. The east - west component of the wind velocity is $v_{wx}=v_w\cos\theta$ and the north - south component is $v_{wy}=v_w\sin\theta$.
$v_{wx}=120\cos30^{\circ}=120\times\frac{\sqrt{3}}{2}= 60\sqrt{3}\approx103.92$ km/h
$v_{wy}=120\sin30^{\circ}=120\times\frac{1}{2}=60$ km/h
The jet is moving at $v_j = 500.0$ km/h due east.

Step2: Calculate the resultant east - west and north - south velocities

The resultant east - west velocity $v_x=v_j + v_{wx}=500+103.92 = 603.92$ km/h. The north - south velocity $v_y = v_{wy}=60$ km/h.

Step3: Use the Pythagorean theorem to find the resultant velocity

The speed of the aircraft relative to the ground $v=\sqrt{v_x^{2}+v_y^{2}}$.
$v=\sqrt{(603.92)^{2}+60^{2}}=\sqrt{364721.77+3600}=\sqrt{368321.77}\approx606.9$ km/h

for Question 8:
The clown and the acrobat are both in the parade. If the acrobat's description of the dumb - bell's motion is very similar to the clown's description, it means that the acrobat and the clown are in the same non - accelerating (constant velocity) frame of reference relative to each other. Since the clown is on the float, and the acrobat's motion description is similar to the clown's, the acrobat is moving with the same velocity as the clown and the float. So the acrobat is at rest with respect to the clown and also at rest with respect to the float.

Answer:

A. $606.9$ km/h