How Can You Correct These Physics Calculation Errors?

[Ultimeaciax]

Out of 20 review questions, I stuck on this three, please help.

A scout troop is practicing its orienting skills with map and compass. First they walk due east for 1.1 km. Next, they walk 45° west of north for 2.1 km. In what direction must they walk to go directly back to their starting point? How far will they have to walk?Ok for what I did: a: x=1.1, y=0; b:-1.5, 1.5 (using sin(45)=O/2.1) a+b= squareroot of 0.4^2 + 1.5^2 = 1.6 That's how far they have to walk.

Angle = sin^-1=1.1/2.1 = 32degree southeast.

What did I do wrong?

Q2. At t = 0, an automobile traveling north begins to make a turn. It follows one-quarter of the arc of a circle of radius 15.0 m until, at t = 1.6 s, it is traveling east. The car does not alter its speed during the turn. Find (a) the car's speed, (b) the change in its velocity during the turn, and (c) its average acceleration during the turn.

a: 1/4*2*pi*15 / 1.6s = 15m/s
b: sqr(15^2+15^2) = 21 m/s southeast
c: 0, because the speed didn't change so there was no acceleration.

I also got that one wrong. What did I do wrong?

3. A 2.30 kg toy locomotive is pulling a 1.60 kg caboose. The frictional force of the track on the caboose is 0.460 N backward along the track. If the train is accelerating forward at 2.50 m/s2, what is the magnitude of the force exerted by the locomotive on the caboose?
This one I have no idea how to approach it.

 

[Ultimeaciax]

Can one help? Maybe just the first question is fine.

 

[Moetasim]

For the first question, the mistake was in the calculation of the angle. To find the angle, you can use the inverse tangent function (tan^-1) instead of the sine function. So the correct angle would be 32 degrees south of east.

For the second question, the mistake was in the calculation of the change in velocity. The correct formula to use is v = rω, where r is the radius and ω is the angular velocity. In this case, the angular velocity can be found by dividing the angle (90 degrees) by the time (1.6 seconds), giving an angular velocity of 56.25 degrees per second. Converting this to radians per second (multiply by π/180), we get an angular velocity of 0.982 radians per second. Then, using the formula v = rω, we get a change in velocity of 15m/s in the direction of the tangent to the circle, which is east.

For the third question, you can use Newton's second law, F = ma, to find the force exerted by the locomotive on the caboose. The mass of the system (locomotive + caboose) is 3.9 kg, and the acceleration is 2.50 m/s2. So the force exerted by the locomotive is F = (3.9 kg)(2.50 m/s2) = 9.75 N. However, since there is a frictional force of 0.460 N acting in the opposite direction, the net force exerted by the locomotive on the caboose is 9.75 N - 0.460 N = 9.29 N.