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When a ball is thrown straight up in the air its height above the ground is given by $s (t) = 12 t - t^{3} + 1$ metres, where $t$ is in seconds, $t \geq 0$ . Find the maximum height reached by the ball.

Important Questions on Measuring Change: Differentiation

MEDIUM

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 5 - Measuring Change: Differentiation>Exercise 5R>Q 2

When a ball is thrown straight up in the air its height above the ground is given by

s (t) = 12 t - t^{3} + 1

metres, where

t

is in seconds,

t \geq 0

. Find the ball's velocity when the ball released.

MEDIUM

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 5 - Measuring Change: Differentiation>Exercise 5R>Q 2

When a ball is thrown straight up in the air its height above the ground is given by

s (t) = 12 t - t^{3} + 1

metres, where

t

is in seconds,

t \geq 0

. Find the ball's velocity when

t = 1

MEDIUM

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 5 - Measuring Change: Differentiation>Exercise 5R>Q 3

When a ball is thrown straight up in the air its height above the ground is given by

s (t) = 12 t - t^{3} + 1

metres, where

t

is in seconds,

t \geq 0

. Find the ball's velocity when

t = 3

MEDIUM

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 5 - Measuring Change: Differentiation>Exercise 5R>Q 4

When a ball is thrown straight up in the air its height above the ground is given by

s (t) = 12 t - t^{3} + 1

metres, where

t

is in seconds,

t \geq 0

. Find the total distance travelled by the ball before it hits the ground.

MEDIUM

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 5 - Measuring Change: Differentiation>Exercise 5R>Q 4

A stone is projected vertically so that its position in metres above ground level after

t

seconds is given by

s (t) = 15 t - 5 t^{2}

. Calculate the time at which the stone reaches its maximum height, and find the maximum height.

MEDIUM

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 5 - Measuring Change: Differentiation>Exercise 5R>Q 4

A person jumps from a diving board above a swimming pool. At time

t

seconds after leaving the board, the person's height above the surface of the pool,

s

metres, can be modelled by the function

s (t) = 10 + 5 t - t^{2}

. Find the height of the diving board above the surface of the pool.

HARD

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 5 - Measuring Change: Differentiation>Exercise 5R>Q 4

A person jumps from a diving board above a swimming pool. At time

t

seconds after leaving the board, the person's height above the surface of the pool,

s

metres, can be modelled by the function

s (t) = 10 + 5 t - t^{2}

. Find the time between the person leaving the board and hitting the water.

HARD

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 5 - Measuring Change: Differentiation>Exercise 5R>Q 4

A person jumps from a diving board above a swimming pool. At time

t

seconds after leaving the board, the person's height above the surface of the pool,

s

metres, can be modelled by the function

s (t) = 10 + 5 t - t^{2}

. Find the velocity and acceleration of the diver upon impact with the water. Interpret your answers in the context of this problem.

When a ball is thrown straight up in the air its height above the ground is given by s(t)=12t-t3+1 metres, where t is in seconds, t≥0. Find the maximum height reached by the ball.

Important Questions on Measuring Change: Differentiation

Learn and Prepare for any exam you want !

When a ball is thrown straight up in the air its height above the ground is given by $s (t) = 12 t - t^{3} + 1$ metres, where $t$ is in seconds, $t \geq 0$ . Find the maximum height reached by the ball.