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A ball of mass m moves towards a ball of mass km with speed u. The coefficient of restitution is 0. What is the final velocity if the first ball after the collision.

Coefficient of restitution is defined as the ratio of the relative speed of separation of the balls to the relative speed of approach. A ratio of 0 means that the speed of separation has a value of zero a...

Answered by Susannah E. • Maths tutor

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Differentiate cos^2(x)

Using the chain rule, Let y=cos²(x)Let u=cos(x)y=u²dy/du=2udu/dx=-sin(x)dy/dx=dy/du*du/dx=-2sin(x)cos(x)

Answered by Manish B. • Maths tutor

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Find the equation of the tangent to the curve x^3+yx^2=1 at the point (1,0).

We can find the gradient of a tangent to a curve at a point by finding dy/dx at x=1.Firstly we can rearrange the equation of the curve for y.(1) yx^2=1-x^3(2)y=x^{-2}-xThen we can differentiate the equati...

Answered by Ollie G. • Maths tutor

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An 1kg ball collides normally with a fixed vertical wall. Its incoming speed is 8 m/s and its speed after the collision is 4 m/s . Calculate the change in momentum of the particle. If the collision lasts 0.5 s calculate the impact force.

Consider two scenarios before and after. Before there is a velocity of 8m/s (with right being positive) and mass 1kg. after there is a mass of 1kg and a velocity of -4 m/s as right is positive and it boun...

Answered by Adam D. • Maths tutor

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A curve has equation y = x^3 - 6x^2 - 15x. The curve has a stationary point M where x = -1. Find the x-coordinate of the other stationary point on the curve.

A stationary point can be found when dy/dx = 0. The first thing we need to do is differentiate y to find dy/dx, and solve it for dy/dx = 0. This gives us...

Answered by Ellie G. • Maths tutor

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