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Alenkinab [10]
2 years ago
5

Two cars, both of mass m, collide and stick together. Prior to the collision, one car had been traveling north at a speed 2v, wh

ile the second was traveling in a southeastern direction at an angle ϕ with respect to the east-west direction and at a speed v. After the collision, the two-car system travels in a northeastern direction at an angle θ with respect to the north-south direction and at a speed vfinal.
Find v_final, the speed of the joined cars after the collision.

Physics
1 answer:
mel-nik [20]2 years ago
7 0

Answer:u=\frac{v}{2}\sqrt{5-4sin\phi }

Explanation:

Given

Both cars mass is m

and solving problem in Vertical and horizontal direction

considering + y and +x to be positive and u be the final velocity of system

Conserving Momentum in Vertical direction

m(2v)+m(-vsin\phi )=2m(ucos\theta )

2ucos\theta =v(2-sin\theta )------1

Conserving momentum in x direction

mvcos\phi =2musin\theta-----2

squaring and adding 1 &2

(2u)^2=(2v-vsin\phi )^2+(vcos\phi )^2

4u^2=4v^2+v^2-4v^2sin\phi

4u^2=5v^2-4v^2sin\phi

u=\frac{v}{2}\sqrt{5-4sin\phi }

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The acceleration of a particle traveling along a straight line isa=14s1/2m/s2, wheresis in meters. Ifv= 0,s= 1 m whent= 0, deter
Yuliya22 [10]

Answer:

0.78m/s

Explanation:

We are given that

Acceleration=a=\frac{1}{4}s^{\frac{1}{2}}m/s^2

v=0, s=1 when t=0

We have to find the particle's velocity at s=2m

We know that

a=\frac{dv}{dt}=\frac{dv}{ds}\times \frac{ds}{dt}=\frac{dv}{ds}v

vdv=ads

\int_{0}^{v} vdv=\int_{1}^{s}0.25s^{\frac{1}{2}}ds

\frac{v^2}{2}=0.25\times \frac{2}{3}(s^{\frac{3}{2})^{s}_{1}

By using formula:\int x^ndx=\frac{x^{n+1}}{n+1}+C

\frac{v^2}{2}=0.25\times \frac{2}{3}(s^{\frac{3}{2}}-1

Substitute s=2

\frac{v^2}{2}=\frac{0.50}{3}((2^{1.5})-1)

\frac{v^2}{2}=\frac{0.50}{3}\times 1.83

v^2=2\times 0.305=0.61

v=\sqrt{0.61}=0.78m/s

Hence, the velocity of particle at s=2m=0.78m/s

3 0
3 years ago
FILL IN TUE BLANK WITH ANSWER DOWN BELOW!!! When storm clouds produce lightning and thunder, 1)_________ energy changes to2)____
kkurt [141]
Electric potential, Chemical , sound
3 0
3 years ago
Read 2 more answers
What was the speed of a space shuttle that orbited Earth at an altitude of 1482 km?
gregori [183]

Answer:

v = 7121.3 m/s

Explanation:

As we know that the centripetal force for the space shuttle is due to gravitational force of earth due to which it will rotate in circular path with constant speed

so here we will have

\frac{mv^2}{r} = \frac{GMm}{r^2}

here we know that

r = orbital radius = 6370 km + 1482 km

r = 7.852 \times 10^6 m

also we know that

M = 5.97 \times 10^{24} kg

now we will have

v^2 = \frac{(6.67 \times 10^{-11})(5.97 \times 10^{24})}{7.852 \times 10^6}

v^2 = 5.07 \times 10^7

v = 7121.3 m/s

3 0
3 years ago
Read 2 more answers
Our body contains ______________ potential energy from food we have eaten.
Alisiya [41]

Answer: Our body contains chemical potential energy from food we have eaten.

This chemical potential energy is transformed into the kinetic energy of our hands and arms as we rub our hands together.

As our hands move past each other and rub against each other, friction allows the kinetic energy to be transformed into thermal energy on the surface of our hands.

Explanation:

It is true that our food contains chemical bonds and these bonds have potential energy stored. So, when we eat food then our body acquires chemical potential energy.

When we rub our hands and arms then they form kinetic energy as atoms present within the skin of our hands come into motion. This rubbing of hands leads to the formation of heat which means thermal energy is being generated.

Thus, we can conclude that our body contains chemical potential energy from food we have eaten.

This chemical potential energy is transformed into the kinetic energy of our hands and arms as we rub our hands together.

As our hands move past each other and rub against each other, friction allows the kinetic energy to be transformed into thermal energy on the surface of our hands.

5 0
3 years ago
The position of a particle moving along the x axis varies in time according to the expression x = 4t 2, where x is in meters and
Pie

Answer:

a) X = 17.64 m

b) X = 17.64 + 4∆t^2 + 16.8∆t

c) Velocity = lim(∆t→0)⁡〖∆X/∆t〗 = 16.8 m/s

Explanation:

a) The position at t = 2.10s is:  

                 X = 4t^2

                 X = 4(2.10)^2

                 X = 17.64 m

b) The position at t = 2.10 + ∆t s  will be:

                 X = 4(2.10 + ∆t)^2

                 X = 17.64 + 4∆t^2 + 16.8∆t  m

c) ∆X is the difference between position at t = 2.10s and t = 2.10 + ∆t so,

                 ∆X= 4∆t^2 + 16.8∆t

Divide by ∆t on both sides:  

                ∆X/∆t =  4∆t + 16.8

 Taking the limit as ∆t approaches to zero we get:  

              Velocity =lim(∆t→0)⁡〖∆X/∆t〗 = 4(0) + 16.8

              Velocity = 16.8 m/s

 

8 0
3 years ago
Read 2 more answers
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