Find the time a ball hits the ground, its velocity at a specific time, and its maximum height given its position function.

Vault Of Euclid

Analyzing the Vertical Motion of a Ball

Rectilinear and curvilinear motion warmup

A ball is thrown vertically upward. Its height \( s \) (in feet) after \( t \) seconds is given by \( s = 40t - 16t^2 \). Find (a) when the ball hits the ground, (b) the instantaneous velocity at \( t=1 \), (c) the maximum height.

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What you need first

Power rule for differentiation
Solving quadratic equations by factoring
Understanding the relationship between position, velocity, and acceleration

What this problem tests

Tests the ability to relate position, velocity, and acceleration, and to use derivatives to find maximum values.

This is a classic introductory calculus problem demonstrating the physical interpretation of the first and second derivatives in kinematics.

Analyzing the Vertical Motion of a Ball

What you need first

What this problem tests

More on Rectilinear and curvilinear motion