Is Mach 2 faster than Mach 33?

Final answer:

The direction in which the torpedo should be fired, as well as the time it will take to reach the battleship, requires solving problems involving relative velocity and kinematics, common in high school physics.

Explanation:

The question is related to the direction and time taken for a torpedo to hit a moving battleship which involves relative velocity and kinematics, a typical topic in high school physics. The submarine should fire the torpedo at an angle calculated using the relative speed and direction of both the torpedo and the battleship to ensure they intersect at a point. The time taken by the torpedo to reach the battleship can then be determined using the relative speeds and the initial distance between them.

Final Answer:

a) The average velocity for the trip is 13.42 m/s, directed at an angle of approximately 243.4° south of west. b) The car's average acceleration during these 3.0 s is approximately 4.47 m/s², directed toward the center of the circle. c) Even though the car's speed is constant, its velocity is changing, resulting in a nonzero average acceleration.

Explanation:

a) To find the average velocity, we need to find the total displacement and divide it by the total time. The total displacement is [tex]\( \frac{3}{4} \)[/tex]of the circumference of the circle, which is [tex]\( \frac{3}{4} \times 2\pi \times 20.0 \)[/tex] m.

Thus, the total displacement is approximately 47.12 m. Dividing this by the total time of 3.0 s gives us the magnitude of the average velocity: [tex]\( \frac{47.12 \, \text{m}}{3.0 \, \text{s}} = 15.71 \, \text{m/s} \)[/tex].

To determine the direction of the average velocity, we use trigonometry. The angle [tex]\( \theta \)[/tex] can be found using the arctangent function: [tex]\( \theta = \tan^{-1}\left(\frac{\text{opposite}}{\text{adjacent}}\right) = \tan^{-1}\left(\frac{20.0 \, \text{m}}{47.12 \, \text{m}}\right) \)[/tex].

Therefore, [tex]\( \theta \approx 63.4^\circ \)[/tex] south of west. Since the car's final velocity is south and its initial velocity is west, the angle of the average velocity is [tex]\( 180^\circ + 63.4^\circ = 243.4^\circ \)[/tex] south of west.

b) The average acceleration can be calculated using the change in velocity divided by the total time.

Since the car's initial and final velocities are perpendicular and the motion is circular, the acceleration is directed toward the center of the circle. The change in velocity can be found by subtracting the initial velocity vector from the final velocity vector.

The magnitude of the change in velocity is [tex]\( \sqrt{v_{fx}^2 + v_{fy}^2} \)[/tex], where [tex]\( v_{fx} \)[/tex] is the final velocity in the x-direction (south) and [tex]\( v_{fy} \)[/tex] is the final velocity in the y-direction (west).

Thus, [tex]\( v_{fx} = 0 \)[/tex] m/s and [tex]\( v_{fy} = -15.71 \)[/tex] m/s. Therefore, [tex]\( \Delta v = \sqrt{0^2 + (-15.71)^2} \, \text{m/s} \)[/tex]. Dividing this by the total time of 3.0 s gives us the magnitude of the average acceleration: [tex]\( \frac{\Delta v}{3.0 \, \text{s}} = \frac{15.71 \, \text{m/s}}{3.0 \, \text{s}} = 4.47 \, \text{m/s}^2 \)[/tex].

c) Even though the car's speed is constant, its velocity is changing because it is moving along a curved path. Velocity includes both speed and direction, so any change in direction, even if the speed remains constant, results in acceleration.

Therefore, the car experiences a nonzero average acceleration due to its change in direction while maintaining a constant speed.

To find the force of gravity, identify the two masses and the distance between them, draw a free-body diagram, and apply Newton's second law of motion or Newton's universal law of gravitation.

To find the force of gravity, you need to identify the two masses involved and the distance between their centers of mass. Following this, you can draw a free-body diagram representing the forces acting on each mass.

Newton's second law of motion is then applied to each mass to determine how it will move. This is done using the equation F = ma, where F is the force, m is the mass and a is the acceleration due to gravity.

You may also use Newton's universal law of gravitation, represented by the equation F = GmM, where F is the gravitational force, G is the gravitational constant, and m and M are the masses of the two objects. Bear in mind that the force of gravity decreases with increasing distance between the objects in proportion to the inverse square of their separation.

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I would've thought all of the above. But if its one answer then go with budgets.