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Yuliya22 [10]
3 years ago
14

At the start of his race, 86-kg Olympic 100m champion Usain Bolt pushes against the starting block, exerting an average force of

1700N. The force that the block exerts on his foot points 20 degrees above the horizontal. Determine his horizontal speed after the force is exerted for 0.32 seconds.
Mathematics
1 answer:
Leviafan [203]3 years ago
3 0
1) Determine the horizontal force, Fx, exerted by the block on Usain

cos(20°) = Fx / F => Fx = F*cos(20) = 1700N*cos(20) = 1597.48 N

2) Determine the Impulse of that force on Usain.

I = F*t = 1597.48N * 0.32s = 511.19 N*s

3) Determine change in momentum of Usain, Δp

Δp = I = 511.19 N*s

4) Find change if velocity

Δp = Δ(mV) = mΔV => ΔV = Δp / m = 511.19 N*s / 86 kg = 5.94 m/s

Given the Usain started from rest, the velocity is ΔV - 0 = 5.94 m/s

Answer: 5.94 m/s
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4 years ago
Fill in the missing work and justification for step 3 when solving 2(x + 1) = 10.
kirill115 [55]

Answer:

2(x + 1) = 10

x = 4

Step-by-step explanation:

Given:

2(x + 1) = 10

Solution:

Apply Distributive property

A*(B+C) = (A*B) + (A*C)

This means multiply 2 with x and 1

2*(x+1) = (2*x) + (2*1)

2x + 2 = 10      

Use Subtraction property of equality

A = B, then A - C = B - C

Subtracting 2 from both sides:

2x + 2 - 2 = 10 - 2

2x = 8                  Step 3

Use Division property of equality

It state that if you divide both sides of an equation by same nonzero number then the sides remain equal

Dividing both sides by 2

2x/2 = 8/2

x = 4

This means value of x is 4

Another method to solve this equation is:

2(x+1)=10  

Use Distributive property

A*(B+C) = (A*B) + (A*C)

2*(x+1) = (2*x) + (2*1)  

2*(x+1) = 2x + 2  

Use commutative property

A + (-B) = (-B) + A

2x + 2 + (-2) = 2x + (-2) + 2

2x + 2 + (-2) = 10 + (-2)

2x + 2 - 2 = 10-2  

2x = 8  

Using division property

AX = B  

AX / A = B / A

So

X = B/A

This becomes:

2x = 8

2x = 8.

Divide both sides by 2  

2x / 2 = 8 / 2  

x = 4

3 0
3 years ago
What is 2 + v/2 = -2?
Artemon [7]

Answer:

v = -8

Step-by-step explanation:

2 + v/2 = -2

Subtract 2 from each side

2-2 + v/2 = -2-2

v/2 =-4

Multiply each side by 2

v/2*2 = -4*2

v = -8

3 0
3 years ago
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