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IceJOKER [234]
3 years ago
8

An object is thrown directly downward from the top of a very tall building. The speed of the object just as it is released is 17

.1 m/s. After being thrown, the object falls freely due to gravity. Neglect air resistance and calculate the distance, in meters which the object covers between times t1 = 3.32 s and t2 = 5.08 s after it is thrown.
Physics
1 answer:
Softa [21]3 years ago
3 0

Answer:

distance cover is  = 102.53 m

Explanation:

Given data:

speed of object is 17.1 m/s

t_1 = 3.32 sec

t_2 = 5.08 sec

from equation of motion we know that

d_1 = vt_1 + \frac{1}{2} gt_1^2

where d_1 is distance covered in time t1

sod_1 = 17.1 \times 3.32 + \frac{1}{2} 9.8 \times 3.32^2=

d_1 = 110.78 m

d_2 = vt_2 + \frac{1}{2} gt_2^2

where d_2 is distance covered in time t2

d_2 = 17.1 \times 5.08 + \frac{1}{2}\times9.8 \times 5.08^2

d_2 = 213.31 m

distance cover is  = 213.31 - 110.78 = 102.53 m

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OLga [1]

A) Car A is initially ahead

B) The two cars are at the same point at the times: t = 0, t = 2.27 s and

t = 5.73 s

C) The distance between the two cars is not changing at t = 1.00 s and t = 4.33 s

D) The two cars have same acceleration at t = 2.67 s

Explanation:

A)

The position of the two cars at time t is given by the following functions:

x_A(t) = \alpha t + \beta t^2

with

\alpha = 2.60 m/s\\\beta = 1.20 m/s^2

Substituting,

x_A(t)=2.60t+1.20 t^2

And

x_B(t)=\gamma t^2 - \delta t^3

with

\gamma=2.80 m/s^2\\\delta = 0.20 m/s^3

Substituting,

x_B(t)=2.80t^2-0.20t^3

Here we want to find which car is ahead just after they leave the starting point. To find that, we just need to calculate the position of the two cars after a very short amount of time, let's say at t = 0.1 s. Substituting this value into the two equations, we get:

x_A(0.1)=2.60(0.1)+1.20(0.1)^2=0.27 m

x_B(0.1)=2.80(0.1)^2-0.20(0.1)^3=0.03 m

So, car A is initially ahead.

B)

The two cars are at the same point when their position is the same. Therefore, when

x_A(t)=x_B(t)

which means when

2.60t+1.20t^2 = 2.80t^2-0.20t^3

Re-arranging the equation, we find

0.20t^3-1.6t^2+2.60t=0\\t(0.20t^2-1.6t+2.60)=0

One solution of this equation is t = 0 (initial point), while we have two more solutions given by the equation

0.20t^2-1.6t+2.60=0

which has two solutions:

t = 2.27 s

t = 5.73 s

So, these are the times at which the cars are at the  same point.

C)

The distance between the two cars A and B is not changing when the velocities of the two cars is the same.

The velocity of car A is given by the derivative of the position of  car A:

v_A(t) = x_A'(t)=(2.60t+1.20t^2)'=2.60+2.40t

The velocity of car B is given by the derivative of the position of car B:

v_B(t)=x_B'(t)=(2.80t^2-0.20t^3)'=5.60t-0.60t^2

Therefore, the distance between the two cars is not changing when the two velocities are equal:

v_A(t)=v_B(t)\\2.60+2.40t=5.60t-0.60t^2\\0.60t^2-3.20t+2.60=0

This is another second-order equation, which has two solutions:

t = 1.00 s

t = 4.33 s

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The acceleration of each car is given by the  derivative of the velocity of the car A.

The acceleration of car A is:

a_A(t)=v_A'(t)=(2.60+2.40t)'=2.40

While the acceleration of car B is:

a_B(t)=v_B'(t)=(5.60t-0.60t^2)'=5.60-1.20t

So, the two cars have same acceleration when

a_A(t)=a_B(t)

And solving the equation, we find:

2.40=5.60-1.20t\\1.20t=3.20\\t=2.67 s

So, the two cars have same acceleration at t = 2.67 s.

Learn more about accelerated motion:

brainly.com/question/9527152

brainly.com/question/11181826

brainly.com/question/2506873

brainly.com/question/2562700

#LearnwithBrainly

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A car has the velocity of 2.35 after 4.67 it's velocity is 9.89 what is the average acceleration
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