Use a=(dv/dt) (change in velocity/ change in time)=acceleration
(1.2/5)=acceleration
F=ma (Newton's second law, Force= Mass x Acceleration
=960 x 0.24 F=230.4N If T<230.4N then the tow rope will hold
Answer is B. According to the equation of motion s = vt + 1/2 at2 Where s is distance covered, v is velocity, a is acceleration and t is time taken. So, by putting all the values, we get s = (20)(5) + 1/2 (3)(5)2 s = 100 + 1/2 (3)(25) s = 100 + 1/2 75 s = 100 + 37.5 s = 137.5 meters
Let's call the constant acceleration a.
At a time t, its speed will thus be v(t)=a*t+v0 where v0 is its initial speed, here 10 m/s. Hence v(t)=a*t+10.
From there we can deduce the position P(t)=a*t^2/2+10t+p0 where p0 is the initial position, here 0.
Hence P(t)=a*t^2/2+10t
Let's call T the time at which it's at 50 m/s, we know that P(T)=225m and that v(T)=50 m/s hence a*T+10=50 thus a=40/T and P(T)=(40/2+10)T=30T
Hence T=225/30=7.5
It took 7.5 seconds
Explanation:
1. To graphically add vectors, use the tail-to-tip method. Draw the first vector (it doesn't matter which), then draw the second vector where the first vector ends. The resultant vector is from the tail of the first vector to the tip of the second vector.
This graph shows two ways to get the resultant: A + B or B + A.
desmos.com/calculator/bqhcclhhqc
2. To algebraically add vectors, split each vector into x and y components.
Aₓ = 5.0 cos 45 = 3.5
Aᵧ = 5.0 sin 45 = 3.5
Bₓ = 2.0 cos 180 = -2.0
Bᵧ = 5.0 sin 180 = 0
The components of the resultant vector are the sums of the components of A and B.
Cₓ = 3.5 + -2.0 = 1.5
Cᵧ = 3.5 + 0 = 3.5
The magnitude of the resultant vector is found with Pythagorean theorem, and the direction is found with tangent.
C = √(Cₓ² + Cᵧ²) ≈ 3.9 m/s
θ = atan(Cᵧ / Cₓ) ≈ 67°
