Projectile Motion h(t) (m) t (s) What is the instantaneous speed of the projectile at each point? 1 4 5 How can we calculate this? 2 3
Calculating the Gradient of a Curve h(t) (m) t (s) Draw a normal to the curve then a tangent at that point. 1 3 4 5 2 normal tangent
Calculating the Gradient of a Curve h(t) (m) t (s) Calculate the gradient of the tangent. 1 3 4 5 normal tangent
Calculating the Gradient of a Curve h(t) (m) t (s) The Rate of Change of the graph is equal to the gradient at that point. tangent (0.5,10) (1.5,20) The gradient of the tangent equals the gradient of the curve at this point. The basketball is travelling at 10m/s at this point.
Gradient Function Use your calculated values for the gradients to complete the following table. x01234 gradient 20100– 10– 20 Now plot these points on squared paper.
Gradient Function You have plotted the value of the gradient at each point x on the curve for 0 ≤ x ≤ 4. This is called the Gradient Function Find the equation of this function.