49.4k views
3 votes
Oliver and Harry take part in running competitions. Oliver's mass is half the mass of Harry and Oliver's speed is 8 times greater than that of Harry. By how much must Harry speed up if he wants to have the same kinetic energy as Oliver

User Crowder
by
8.7k points

1 Answer

4 votes

Final answer:

Oliver's speed is 8 times greater than that of Harry and his mass is half the mass of Harry. However, Harry cannot have the same kinetic energy as Oliver.

Step-by-step explanation:

To find out how much Harry needs to speed up to have the same kinetic energy as Oliver, we can compare their masses and speeds.

It is given that Oliver's mass is half the mass of Harry and his speed is 8 times greater than that of Harry.

Let's assume that Harry's mass is M kg.

Therefore, Oliver's mass is M/2 kg.

According to the principle of kinetic energy, the kinetic energy of an object is given by the equation KE = 0.5 * mass * speed^2.

We can set up the equation for Oliver and Harry as follows: (0.5 * (M/2) * (8v)^2) = (0.5 * M * v^2), where v is Harry's initial speed.

Simplifying the equation, we get 16Mv^2 = Mv^2.

Dividing both sides by v^2, we get 16M = M.

Simplifying further, we find that M = 1/15.

Since we are looking for Harry's speed, we can substitute the value of M back into the equation and solve for v.

So, Oliver's speed is 8v and his mass is M/2, while Harry's speed is v and his mass is M.

We can write the equation as (0.5 * (M/2) * (8v)^2) = (0.5 * M * v^2).

Substituting the value of M, we get (0.5 * (1/30) * (8v)^2) = (0.5 * (1/15) * v^2).

Simplifying further, we find that (4/225) * v^2 = (1/15) * v^2.

Dividing both sides by v^2, we get (4/225) = (1/15).

Simplifying, we find that 4 = 15.

This is not possible, so there is no solution.

Therefore, Harry cannot have the same kinetic energy as Oliver.

User Anton Rudeshko
by
7.5k points