IAL differentiation(?) question

The height of sea water, h metres, on a harbour wall at time t hours after midnight is given by
h = 3.7 + 2.5cos(30t – 40)°, 0 < t < 24

(a) Calculate the maximum value of h and the exact time of day when this maximum first occurs.

Fishing boats cannot enter the harbour if h is less than 3

(b) Find the times during the morning between which fishing boats cannot enter the harbour. Give these times to the nearest minute

Okay, how on Earth are you supposed to do this?

Reply 1

Zacken

22

Original post by jessyjellytot14

The height of sea water, h metres, on a harbour wall at time t hours after midnight is given by
h = 3.7 + 2.5cos(30t – 40)°, 0 < t < 24

(a) Calculate the maximum value of h and the exact time of day when this maximum first occurs.

Fishing boats cannot enter the harbour if h is less than 3

(b) Find the times during the morning between which fishing boats cannot enter the harbour. Give these times to the nearest minute

Okay, how on Earth are you supposed to do this?

You should be familiar with these sort of Rcos(x - a) questions.

Cosine is bounded between -1 and 1.

-2.5 < 2.5 cos (anything) < 2.5

So 3.7 -2.5 < 3.7 + 2.5 cos (anything) < 3.7 + 2.5

That's yur maximum right there. This occurs when cos (anything) = 1 (for part(b)) so solve thatz.

Reply 2

jessyjellytot14

OP

17

Original post by Zacken

You should be familiar with these sort of Rcos(x - a) questions.

Cosine is bounded between -1 and 1.

-2.5 < 2.5 cos (anything) < 2.5

So 3.7 -2.5 < 3.7 + 2.5 cos (anything) < 3.7 + 2.5

That's yur maximum right there. This occurs when cos (anything) = 1 (for part(b)) so solve thatz.