Question

Use the Pythagorean theorem to answer this question. Becca paddles a boat from the south bank of a stream to the north bank. She paddles at a rate of 8 mph. The stream is flowing west at a rate of 6 mph. What is Becca's actual velocity?

Andrew kicks a ball along a straight path. The ball rolls straight forward for 13.2 meters. Then Andrew kicks the ball straight back. The ball rolls back along the same path for 9.5 meters. What distance did the ball travel?

Answer 1

Answer:

Question 1:

Becca paddles a boat from the south bank of a stream to the north bank. She paddles at a rate of 8 mph. The stream is flowing west at a rate of 6 mph. What is Becca's actual velocity?

Answer 1:

Boat is travelling from South to the north of the stream.

The speed of the boat is 8 mph.

The speed of the stream towards west is 6 mph.

Here, the boat is trying to go pendicularly, but because of the speed of the stream towards the west, the boat while travelling will bend towards that direction.

The actual velocity of the boat can be found out by the hypotenuse of the right angled triangle formed by the given information.

So, A² + B² = H²

⇒ 8² + 6² = H²

⇒ H = √(8² + 6²)

⇒ H = √(64 + 36)

⇒ H = √100

⇒ H = 10 mph

So, the actual velocity of the boat is 10 mph.

Question 2:

Andrew kicks a ball along a straight path. The ball rolls straight forward for 13.2 meters. Then Andrew kicks the ball straight back. The ball rolls back along the same path for 9.5 meters. What distance did the ball travel?

Answer 2:

Distance from point A to point B = 13.2 m

Distance from point B to point C = 9.5 m

We need to find the total distance travelled by the ball.

So, Total Distance = 13.2+9.5 = 22.7 m.

Hence, the distance travel by the ball = 22.7 m.

Answer 2

Answer:

Question No 1 :-

• Using the Pythagorean Theorem to answer this question.
• Becca paddles a boat from the south bank of a stream to the north bank. She paddles at a rate of 8 mph. The stream is flowing west at a rate of 6 mph. What is Becca's velocity.

Given :-

• Becca paddles a boat from the south bank of a stream to the north bank.
• She paddles at a rate of 8 mph. The stream is flowing west at a rate of 6 mph.

To Find :-

• What is the Becca's velocity.

Formula Used :-

$\clubsuit$ Pythagorean Theorem :

$\mapsto \sf\boxed{\bold{\pink{(Perpendicular)^2 + (Base)^2 =\: (Hypotenuse)^2}}}$

Solution :-

Given :

$\bigstar\: \: \sf Perpendicular =\: 8\: mph$

$\bigstar\: \sf Base =\: 6\: mph$

According to the question by using the pythagorean theorem we get,

$\longrightarrow \sf (8)^2 + (6)^2 =\: (Hypotenuse)^2$

$\longrightarrow \sf 8 \times 8 + 6 \times 6 =\: (Hypotenuse)^2$

$\longrightarrow \sf 64 + 36 =\: (Hypotenuse)^2$

$\longrightarrow \sf 100 =\: (Hypotenuse)^2$

$\longrightarrow \sf \sqrt{100} =\: Hypotenuse$

$\longrightarrow \sf 10 =\: Hypotenuse$

$\longrightarrow \sf\bold{\red{Hypotenuse =\: 10\: mph}}$

$\therefore$ The actual velocity is 10 mph .

Question No - 2 :-

• Andrew kicks a ball along a straight path. The ball rolls straight forward for 13.2 metres. Then Andrew kicks the ball straight back. The ball rolls back along the same path for 9.5 metres. What is the distance did the ball travel.

Given :-

• Andrew kicks a ball along a straight path. The ball straight forward for 13.2 metres. Then Andrew kicks the ball straight back. The ball rolls back along the same path for 9.5 metres.

To Find :-

• What is the distance did the ball travel.

Solution :-

$\mapsto$ First, Andrew kicks a ball along a straight path. The ball straight forward 13.2 metres.

$\mapsto$ Again, Andrew kicks the ball straight back. The ball rolls back along the same path for 9.5 metres.

Then, the distance did the ball travel is :

$\longrightarrow \sf Distance\: travel\: by\: the\: ball =\: 13.2\: metres + 9.5\: metres$

$\longrightarrow \sf Distance\: travel\: by\: the\: ball =\: \dfrac{132}{10}\: + \dfrac{95}{10}\: metres$

$\longrightarrow \sf Distance\: travel\: by\: the\: ball =\: \dfrac{132 + 95}{10}\: metres$

$\longrightarrow \sf Distance\: travel\: by\: the\: ball =\: \dfrac{227}{10}\: metres$

$\longrightarrow \sf\bold{\red{Distance\: travel\: by\: the\: ball =\: 22.7\: metres}}$

$\therefore$ The distance travel by the ball is 22.7 m .