Answer:
Ive left an image here for use, I hope its helpful
Explanation:
I have left two images and i hope i am answering your question.
Answer:
The maximum speed will be 26.475 m/sec
Explanation:
We have given mass of the toy m = 0.50 kg
radius of the light string r = 1 m
Tension on the string T = 350 N
We have to find the maximum speed without breaking the string
For without breaking the string tension must be equal to the centripetal force
So 
So 

v = 26.475 m /sec
So the maximum speed will be 26.475 m/sec
Answer:
V = 20 miles /sec
Explanation:
We have remaining distance = d = 96 miles
Lets call Pascal velocity V in miles per hour
Now if he increases his velocity by 50 % (equivalent to multiply by 1.5 ) he will need a time t₁ to arrive then as V = d/t
1.5* V = d/ t₁ ⇒ 1.5 * V = 96 /t₁
And in the case of reducing his velocity
(V / 4) = d/ (t₁ + 16 ) ⇒ V * (t₁ + 16 ) = 4*d ⇒ V*t₁ + 16*V = 384
So we a 2 equation system with two uknown variables
1.5*V = 96/t₁ (1)
V*t₁ + 16*V = 384 (2)
We solve from equation (1) t₁ = 64/V
And by substitution in equation (2)
V * (64/V) + 16* V = 384
64 + 16 *V = 384 ⇒ 16*V = 320 ⇒ V= 320/16
V = 20 miles /sec
Since force is mass*acceleration,
F = 70kg * 9.8 m/s