1. Wile E. Coyote launches a water balloon from the top of a 140-foot tall building with an initial velocity of 50 ft/s. Assuming an acceleration due to gravity of –32 ft/s² and no wind resistance, (a) Solve an initial value problem to find v(t), the velocity of the water balloon at time t. (b) Solve an initial value problem to find s(t), the height of the water balloon at time t. (c) At what time does the water balloon reach its highest point? How high is it at that point? (d) The Road Runner, who is 2 feet tall, is standing underneath the falling water balloon. If he doesn't move out of the way in time, how fast will the water balloon be going when it hits him on the top of the head?

Q: A ball is tossed straight up in the air. The ball reaches a maximum height of 1 meter. Which of the…

A: Given that a ball is tossed straight in the air. The ball reaches a maximum height of 1 meter.

Q: A particle has acceleration a(t) = eº.¹ti + 12tk. If its initial velocity is i - 3j and its initial…

A:

Q: - ☐ 10. A car which begins at position d = 0, travels according to the following velocity function:…

A: Step 1:Step 2: Step 3: Step 4:  thanks 🙏💛

Q: Suppose an object is moving along a line such that the acceleration after t seconds is 6t -8t…

A:

Q: A force of 720 newtons stretches a spring 4 meters. A mass of 45 kilograms is attached to the end of…

A: The equation of the spring mass system with noo external force is:md2xdt2+kx=0, x(0)=0, x'(0)=-6m/s…

Q: 3. A particle moves along the x-axis. At time t seconds, its acceleration is given by a = 4t + 67/2,…

A:

Q: 6) A weight oscillates in a vertical motion according to the position function y(f) = -5 cos t.…

A: Acceleration for position function yt=-5cost is d2ydt2. Calculate double derivative d2ydt2 and…

Q: A pulley and two loads are connected by inextensible cords as shown. Load A has a constant…

A:

Q: An object with an initial velocity of v(0) = 3 has an acceleration of a(t) = 5 + 6t. What is its…

A: Relationship between velocity and acceleration

Q: A point on the parabola y=ax²+bx+c, where a = 5, b = 5, and c = 2, is moving with uniform horizontal…

A: The point moves on a parabolic path.

Q: 1. A model for the position x (t) of an Olympic jump skier says that the acceleration a(t) = x" is…

A: As per as our guidelines i am supposed to answer only three parts of this question Please repost the…

Q: Table Q3: Interest rate offered by a private bank of over 6 years time 2017 6.50 2019 4.85 2020 Year…

A:

Q: A mass weighing 16 pounds stretches a spring feet. The mass is initially released from rest from a…

A: Let m be the mass attached, k be the spring constant and β be the positive damping constant. 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.