I need part d and e I'm unable to transcribe the entire text directly from the image, but I can describe and explain the content.---### Educational Exercise on Implicit Differentiation and Related Rates**Problem 13: Shot Put Problem**- **Scenario:** A man throws a shot put with an initial velocity of 55 ft/sec. The height is modeled by the equation \( s(t) = 32t + 55t - 16t^2 \). - **Tasks:** - **a.** Find the velocity \( v(t) \) as a function of time. - **b.** Determine the shot’s speed at a given time. - **c.** Calculate the acceleration at time \( t \). - **d.** Find the time when the shot hits the ground and round to the nearest tenth. - **e.** Calculate the velocity when it hits the ground.**Solution Steps:**- Derivative calculations for velocity and acceleration.- Solving a quadratic equation to find when it hits the ground.**Problem 14: Implicit Differentiation**- **Task:** Consider a curve defined by the equation \( x^2y - 3x^2 - 6y = 0 \). - **a.** Use implicit differentiation to find \( \frac{dy}{dx} \). - **b.** Determine the slope of the curve at \( (-1, 1) \).**Solution Steps:**- Differentiate both sides with respect to \( x \) and solve for \( \frac{dy}{dx} \).**Problem 15: Related Rates Problem**- **Scenario:** Sand falls from a conveyor belt at a rate of 12 \(\text{m}^3/\text{min}\) onto the top of a conical pile. The radius of the base is always three-fourths the height of the pile. - **Task:** Determine how fast the height of the pile is changing when the height is 4 m.- **Concept:** Use the relationship between the volume of the cone and its parameters.**Solution Steps:**- Write the volume of a cone formula \( V = \frac{1}{3} \pi r^2 h \).- Establish relations between the height and the radius.- Differentiate with respect to time to find rates of change.### Notes on Diagrams- The image includes handwritten solutions

d. Note that at the ground, s(t) = 0 The time taken by the shot to hit the ground is calculated in the following way.e. The velocity of the ball when it strikes the ground is calculated in the following way. Here, the negative sign shows that the direction of velocity is downwards.

Science

Physics

13. A 6 ft tall man throws a shot put with an initial velocity of 55 f/sec. The height of the shot after t seconds can be modeled by s(t) = 6+55t - 16t2. a. Find the shot's velocity at time t. V=-32t+55 b. Find the shot's speed at timę t. V= S'(E) =-32七+55 t: %3D 5. O= 6+556-L O=-16t+55 1-32t+55 c. Find the shot's acceleration at time t. -32 FEIS2 d. How long will it take the shot to hit the ground? Round the answer to the nearest tenth of a second. e. What is the velocity of the ball when it hits the ground?