Answer: Tension = 47.8N, Δx = 11.5×
m.
Tension = 95.6N, Δx = 15.4×
m
Explanation: The speed of a wave on a string under tension can be determined using the following:
denotes tension (N)
μ refers to linear density (kg/m)
Calculating the velocity:
0.0935 m/s
Distance a pulse traveled in 1.23ms:
Δx = 11.5×
With a tension of 47.8N, the distance a pulse will cover is Δx = 11.5× m.
When tension is doubled:
|v| = 0.1252 m/s
Distance in the same time:
15.4×
With the increased tension, it moves 15.4× m
Answer:
The driveway measures 4.98 m
Explanation:
We aim to find the length of the driveway, thus utilizing the following equations
W=ΔK.E where W represents work and ΔK.E indicates the change in kinetic energy
Moreover,
also
W = F.d where F is the force and d denotes distance
Given that
= 4000 N indicating this frictional force
m = 2100 Kg
θ= 20.0°
V=3.8 m/s representing the car's speed at the bottom of the driveway
W=Δ K.E
= 15162 J
As the x component of gravity is
= mg sinФ
thus
= (2100)(9.8)sin(20.0°) results in
= 7038.77 N
And the Net force is
=
-
= 7038.77 - 4000 = 3038.77 N
So, the length of the driveway equals W / (
) = 15162/3038.77 = 4.98 m
Thus, this is the length of the driveway.
Answer:
The direction in which a vehicle accelerates aligns with its velocity direction. However, the force of acceleration works against the car's speed.
Explanation:
The car’s initial acceleration can be found using:
v = v₀ + a t
a = (v-v₀) t
which assumes the initial speed is zero (v₀ = 0 m/s).
a = v / t
a = 300 / t
The acceleration vector matches the direction of the vehicle's movement.
Upon hitting the wall, a force is exerted in the reverse direction to halt the car, thus this acceleration opposes the vehicle’s speed. However, the module should be much greater since the stopping distance is minimal.
Answer:
a. Angle= 28.82°
b. Approved. Although he might feel cold, he should be able to cross.
Explanation:
Velocity Vector
Velocity is a measure of how quickly something is moving in a specific direction. It is represented as a vector that has both magnitude and direction. If an object can only move in one direction, then speed can serve as the scalar equivalent of that velocity (only focusing on magnitude).
a.
The explorer aims to swim across a river to reach his campsite, as depicted in the image below. The river's velocity is vr and the explorer's swimming speed in still water is ve. If he were to swim straight towards the campsite, he would end up downstream due to the river's current. Therefore, he must swim at an angle that allows him to overcome the current while still moving towards his goal. This angle relative to the shore is what we need to determine. The explorer's speed can be broken down into its horizontal (vx) and vertical (vy) components. In order to counteract the river's flow:
We can calculate the vertical component of the explorer's swimming speed as
Thus
Finding the value of 
Then the angle is given by
b.
The component of the explorer's velocity that goes horizontally is
This represents the actual velocity directed towards the campsite
Considering that
To find t
Calculating the duration for the explorer to cross the river
As this time is under the hypothermia threshold (300 seconds), the conclusion is
Approved. Although he will feel cold, he should manage to cross successfully.
Answer:
The car that is the furthest from the finish line is: Car III (Choice C).
Explanation:
Here, we seek the car with the lowest overall average speed throughout the race. Thus, the one in last place inherently possesses the slowest average speed.
Since Car III is significantly behind Cars I and II, Choice A and B cannot be correct. Choice D is also not valid, as the positions of the cars are not the same. Lastly, Choice E is incorrect due to sufficient evidence demonstrating that Choice C has the lowest average speed.
