Need help with 3 and 4 specifically, but additional help on 1 and 2 is appreciated.
3. The figure shows the graphs of three functions. One isthe position of a car, one is the velocity of the car, andone is its acceleration. Identify each curve and explainyour choices.For problem 4, use the position function p(𝑡) = −16𝑡2 + 𝑣0𝑡 + p0, where s is measured in feet, t in
the position of a car, one is the velocity of the car, and
one is its acceleration. Identify each curve and explain
your choices.
For problem 4, use the position function p(𝑡) = −16𝑡2 + 𝑣0𝑡 + p0, where s is measured in feet, t in
- Need Help With 3 And 4 Specifically But Additional Help On 1 And 2 Is Appreciated 3 The Figure Shows The Graphs Of Th 1 (58.89 KiB) Viewed 115 times
Math 1426 Problem Solving Lab 4 Summer 2022 1. The formula h(t) = -16t² + 480t, describes a model rocket's height. h(t) is the rocket's height measured in feet from the ground, t seconds after take-off. a. Sketch the graph of h(t) for t20. After how many seconds does the rocket impact the ground? b. Find the velocity function () of the rocket. c. Sketch the graph of (t) and interpret it based on the rocket's actual motion. d. Compute the rocket's velocity at t=0, t= 15, and t= 18, How do you interpret the signs of the values you obtained? e Sketch the graph of s(t), the speed function. Find the rocket's speed at t=0, t = 15, and t = 18. f. After how many seconds will the rocket start falling? Use differentiation to find the maximum height attained by the rocket. g. After how many seconds will the rocket hit the ground? What is its velocity at that moment? h. Determine the rocket's acceleration, a(t). Why does it make sense that a(t) is constant and negative? Explain. 2. You are traveling down a country road at a rate of 95 feet/sec when you see a large cow 300 feet in front of you and directly in your lane. The cow is fearless, and staring you down. (Or perhaps she does not understand the gravity of the situation.) Regardless, if you simply hit your brakes, after t seconds, the car will be j(t)=951-9t^2 feet from the point where the brakes were first applied. (i) Must you steer to avoid the cow, or can you rely solely on your brakes? Explain. (ii) Graph j(t), j'(t), and j"(t) and interpret their meanings in context. (iii) Is there a time t after which the graphs in part (ii) probably do not accurately model the path of the car? (iv) Write a piece-wise function using j(t) that would more accurately model the path of the car on the interval [0,10), assuming the car did not move after it stopped. Sketch this graph and its derivative. p 3. The figure shows the graphs of three functions. One is the position of a car, one is the velocity of the car, and one is its acceleration. Identify each curve and explain your choices. For problem 4, use the position function p(t)=-16t+at+Po. where s is measured in feet, tin seconds and 1 and po are the initial velocity and position respectively. 4. A professional baseball pitcher was capable of throwing a baseball 160 ft/s. During his career, he had the opportunity to pitch in the Houston Astrodome. The Astrodome was an indoor stadium with a ceiling 208 ft. high. a. Could the pitcher have hit the ceiling of the Astrodome if he were capable of giving a baseball an upward velocity of 100 ft/s from a height of 7.5 ft? b. How fast would the pitcher have to throw a ball upward from a height of 7.5 feet in order to hit the ceiling of the Astrodome?