A rocket is fired into the air from a table that is 3 feet above the ground with an initial velocity of 100 feet per second. This means that the position function is: h(t)=-16t^2 +100t+3 where the time t is measured in seconds. a)Find the velocity of the rocket when t= 2 seconds. b)Find the acceleration of the object when t = 2 seconds.

Q: A rock is thrown in the air. The height is measured until it returns to the ground 9 seconds later.…

A: The height of the rock is measured by the function .We have to find,(a) The velocity of the rock…

Q: A motorist starts braking for a stop sign. After t seconds, the distance, in metres, from the front…

A: The given equation is s(t)=62-16t+t2. The distance between the front of the car and the stop sign…

Q: The graph below shows the velocity v in feet per second of a small rocket that was fired from the…

A:

Q: A firefighter holds a hose 3 m off the ground and directs a stream of water toward a burning…

A:

Q: A ball is thrown downward with a speed of 11 ft/s from the top of a 121-foot-tall building. After t…

A:

Q: a.)A construction worker dropped his laptop off the top of a high-rise office building. The height,…

A: A construction worker dropped his laptop off the top of a high-rise office building. The height,  in…

Q: 1) Football travels through the air followed by the function h(t)= -4.9t^2+16t+1 where h is the…

A: Given , football travel followed by the function  h(t) =-4.9t2 +16t +1       .. .. .. .. .. ..(1)…

Q: The equation M(x,y) = 73 +0.8x -0.9y gives the mileage (in mpg) of a new car as a function of tire…

A:

Q: A newborn baby weighed 10 pounds at birth and was 15 inches tall. After 7 months the baby weighs 17…

A:

Q: Determine the particular equation for the velocity if the acceleration is given by the equation a =…

A:

Q: An object moving along a horizontal coordinate line has directed distance s(t) = t - 6t2 + 9t + 11…

A: s(t)=t3-6t2+9t+11 Differentiating with respect to t s'(t)=ddt(t3-6t2+9t+11)=3t2-6*2t+9+0=3t2-12t+9…

Q: The windchill index announced during the winter by the weather bureau measures how cold it "feels"…

A:

Q: When an air conditioner is turned on maximum in a bedroom al 82", approximated by the function T(A)=…

A: Given room temperature after the AC turned on after 'A' minutes is T(A)=-0.02A2-0.35A+82 where…

Q: by John throws a football off the roof Of the gym to a spot on the ground, The height of the ball is…

A: The height of the ball is modelled by the function h(t) = -5t² + 20t+15 where h is the height in…

Q: If the initial velocity of a projectile is 96 feet per second, then its height in feet is a function…

A: Approach to solving the question:Please see attached photos for detailed solutions. Thank you.…

Q: The robotic arm you are working with extends to pick up components at various speeds. Its extension…

A: Step 1: Step 2: Step 3: Step 4:

Q: An 80-year-old athlete has his speed in km/h modeled by the function f(t) = -t^2 + 16t, where t is…

A: An 80-year-old athlete has his speed in km/h modeled by the function f(t)=-t2+16t, where t is the…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.