An athlete launches a shot put from shoulder height. The height of the shot put, in metres, above the ground t seconds after launch, can be modelled by the following function: h(t) = 1.7 + 10t − 5t² t > 0

a. Give the physical meaning of the constant term 1.7 in the context of the model.

b. Use the model to calculate how many seconds after launch the shot put hits the ground.

c. Rearrange h(t) into the form A − B(t − C)² and give the values of the constants A, B and C.

d Using your answer to part c or otherwise, find the maximum height of the shot put, and the time at which this maximum height is reached.