Question

A golfer hits a 42 g ball, which comes down on a tree root and bounces straight up with an initial speed of 15.6 m/s. Determine the height the ball will rise after the bounce. Show all your work.​

Answer 1

AnswEr :

• The height of the ball will rise the bounce = 12.41 m.

⠀

Explanation :

We are given with the mass, initial velocity, final velocity, and acceleration due to gravity of a ball, that is,

• Mass of ball, m = 42 g.

⠀

• Initial velocity of ball, u = 15.6 m/s.

⠀

• Final velocity of ball, v = 0 m/s.

⠀

• Acceleration due to gravity, g = 9.8 m/s².

We have to find out the height of the ball will rise the bounce.

⠀________________________

We know that, if we are given with the mass of a ball, initial velocity of ball, final velocity of ball, and acceleration due to gravity, we know the third equation of motion, that is,

⠀

⠀

$\rm{\hookrightarrow v^2 = u^2 + 2gh}$

⠀

⠀

Substituting the given values in the formula :

⠀

$\tt{:\implies 0^2 = 15.6^2 + 2 \times (-9.8) \times h}$

⠀

$\tt{:\implies 0 = 243.36 + 2 \times (-9.8) \times h}$

⠀

$\tt{:\implies 0 = 243.36 + ( - 19.6) \times h}$

⠀

$\tt{:\implies 0 = 243.36 - 19.6 \times h}$

⠀

$\tt{:\implies -243.36 = - 19.6 \times h}$

⠀

$\tt{:\implies -243.36 = - 19.6 \times h}$

⠀

$\tt{:\implies -243.36 = -19.6h}$

⠀

$\tt{:\implies h = \dfrac{ \cancel- 243.36}{ \cancel- 19.6} }$

⠀

$\tt{:\implies h = \cancel{\dfrac{243.36}{19.6} }}$

⠀

$\tt{:\implies \boxed{ \frak{ \pink{h = 12.41 \: m}}}}$

⠀

Hence, the height of the ball will rise the bounce is 12.41 m.

Answer 2

$\huge{\boxed{\rm{Question}}}$

A golfer hits a 42 g ball, which comes down on a tree root and bounces straight up with an initial speed of 15.6 m/s. Determine the height of the ball will rise after the bounce. Show all your work.

$\huge{\boxed{\rm{Answer}}}$

$\large{\boxed{\boxed{\sf{Given \: that}}}}$

• Mass of the ball = 42 grams.

• Initial velocity of the ball = 15.6 m/s.

• Final velocity of the ball = 0 m/s.

• Acceleration due to gravity = 9.8 m/s².

$\small{\boxed{\boxed{\sf{R \: u \: confused \: with \: the \: result \: of \: final \: velocity \: as 0m/s}}}}$

$\small{\boxed{\boxed{\sf{Yes \: we \: r \: little \: bit \: confused}}}}$

$\small{\boxed{\boxed{\sf{No \: need \: to \: worry \: let's \: see \: why \: the \: result \: is \: like \: this}}}}$

✞ The result is 0 m/s means the final velocity is 0 m/s because the ball is in rest at this time. That's why the final velocity will be 0 m/s.

$\large{\boxed{\boxed{\sf{To \: find}}}}$

• The height of the ball will rise after the bounce.

$\large{\boxed{\boxed{\sf{Solution}}}}$

• The height of the ball will rise after the bounce = 12.41 metres.

$\large{\boxed{\boxed{\sf{We \: also \: write \: these \: as}}}}$

• Gravity as g

• Final velocity as v.

• Initial velocity as u.

• Acceleration as a

$\large{\boxed{\boxed{\sf{What \: does \: the \: question \: says}}}}$

$\large{\boxed{\boxed{\sf{Let's \: understand \: the \: concept \: 1st}}}}$

• This question says that a golfer hits a ball and the mass of the ball is 42 g , which comes down on a tree root and bounces straight up with an initial speed of 15.6 m/s. Afterthat we have to determine the height the ball will rise after the bounce. In short we have to find the height the ball will rise after the bounce.

$\large{\boxed{\boxed{\sf{How \: to \: solve \: this \: problem}}}}$

$\large{\boxed{\boxed{\sf{Let's \: see \: the \: procedure \: now}}}}$

• To solve this question we have to use the formula of Newton's third law of motion and its v² = u² + 2gh. Now according to this formula we have to put the values and at last we get our result very easily. And we get 12.41 m as our final result. Means 12.41 is the h of the ball will rise after the bounce.

$\large{\boxed{\boxed{\sf{Full \: solution}}}}$

✞ According to the question we already know that what is given or what to find. Let's see it again !

• Mass of the ball ( Given )

• Final velocity ( Given )

• Initial velocity ( Given )

• Acceleration due to gravity ( Given )

• Height of the ball will rise after the bounce ( Find )

✞ To solve this question we know we have to use the formula of Newton's third law of motion and we know that what is its formula . The formula is given below ➝

• v² = u² + 2gh.

Now we have to out the values according to this formula ➝

➨ v² = u² + 2gh.

➨ 0² = 15.6² + 2 × ( -9.8) × h

➨ 0 = 243.36 + 2 × ( -9.8) × h

➨ 0 = 243.36 + (-19.6) × h

➨ 0 = 243.36 - 19.6 × h ( + - = - )

➨ -243.36 = - 19.6 × h

➨ -243.36 = -19.6h

➨ h = -243.36 / -19.6

➨ h = 243.36 / 19.6 ( - - = + )

➨ h = 12.41 metres.

$\bold{\green{\fbox{\green{Height = 12.41 metres}}}}$

Hence, 12.41 metres is the height of the ball will rise after the bounce.