. [P] In R2, we are throwing a ball att = 0 from the point (0, h) towards the positive r direction. Our initial speed will be 10 m/s and our initial velocity vector makes an angle of 0 with the r-axis. The only acceleration acting on the ball is due to gravity, which we can approximate as a(t) = (0, –10). Our goal is to make a formula which will tell us where the ball lands, as a function of h and 0. (a) What is the initial velocity of the ball? (b) Find a parametric function for the position of the ball at time t; leave h and 0 as unknown constants throughout. (c) Find the time T at which the ball hits the r-axis as a function of h and 0. (d) Find the r-coordinate where the ball hits the r-axis as a function of h and 0. (e) [S] [C] Calculate where the ball lands if launched from a height of 5.3 meters and with an angle of 37°.

Q: where is in seconds, and v is a. Is the particle speeding up or slowing down at t = 5? b. If the…

A: Given that a particle is moving along a horizontal line such that its velocity is given by…

Q: The position of a particle moving along the x-axis is given by 4 37 x(t) = (t – 1)* +(t – 1)³ – 12(t…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: A particle moves along the curve *= 21² , y = t² – 4t and = = 31 – 5 where t is the time . Find the…

A: Given: Position vector is given as, r→=2t2i^+(t2-4t)j^+(3t-5)k^ The objective is to find the…

Q: If the velocity is given by : (-t^2 i + 2t^2 j+ t^2 k) then the normal component of the acceleration…

A: Given: Velocity: vt=-t2i+2t2j+t2k. Then, v't=-2t i+4t j+2t k Find the normal component of the…

Q: 9. What is the relation between the acceleration a(t) and velocity V(t) at a given time t? [C:2]

A:

Q: If v(t) = 4t + 3t – 1 is the velocity of an object over time, what is the acceleration of the object…

A: Note: As per the company guidelines we can solve only 1st question please repost the 2nd question…

Q: a) What is the particle's position at time 2? b) What is the particle’s displacement from t= 1 to…

A: (a) The function representing the position is  X(t)=t3-15t2+48t. To find the position of the…

Q: 2. A particle is moving along a horizontal line such that its velocity is given by v(t) = 3t2 –…

A: Topic:- application of derivatives and integration

Q: Find the equation of the tangent plane to z = ey + x + x2 + 11 at the point (5, 0, 42).

A:

Q: Given the acceleration of a particle is a(t) = . If the initial velocity is v(0) = and the initial…

A: Givena(t) = <3,9t,et>

Q: Given a small disk (2-Kg) sliding on top of a smooth table which is connected to an elastic cord…

A:

Q: The equation of the tangent line to the curve y = 1 at the point (3,-) is Vx +1 A. x+16y +11=0 B. x+…

A: Please refer the attached solution. None of the option is correct here . I have solved it…

Q: An object with an initial velocity of v(0) = 5 has an acceleration of a(t) = t² - 5. What is its…

A: Concept: The acceleration is given by the derivative of the velocity  That is a(t)=dv(t)dt Thus…

Q: The time of oscillation, 1, of a pen- dulum is given by t 27 1. wherel is the length %3D of the…

A: Write this equation in standard form then diffrenciate.

Q: The acceleration of a particle at time t is given by a(t) = 4e2t¸ If the initial velocity was 5, and…

A: We will use integration to first find the velocity and then integrate velocity function to find…

Q: The temperature at a point on a metal surface is T (x, y. z) = 0.05x² – 0.01y³ – z in degrees…

A:

Q: Given the acceleration a=d^2s/dt^ 2​, initial​ velocity, and initial position of a body moving on a…

A: Given :- a=-81sin9t, v(0)=9,  s(0)=-7 Here, a is accelerationdvdt, v is velocity dsdt and s is…

Q: The slope of the tangent to the curve r = 3 sin 40 at 0 = 0 is %3D Şelect one: O a. -1 3D1 O b. 0 C.…

A:

Q: A particle moves on the x-axis with velocity given by v(t) = 3t4 − 11t2 + 9t − 2 for −3 ≤ t ≤ 3 .…

A:

Q: An object with a mass of 10.00kg is launched from the ground with an initial upward velocity of…

A:

Q: c, d

A:

Q: Find the velocity and acceleration vectors and the equation of the tangent line for the curve r(t) =…

A: we are given the curve r(t)=3ti+e4tj+6e-tk we have to find the velocity vector , acceleration vector…

Q: - The position of an object moving on a line is given by s(t) = 6t2 – t°, t > 0,

A: Solve

Q: The position of a particle moving along a coordinate axis is given by s(t)=t^3−9t^2+24t+4 for t≥0.…

A: For velociti differentiation of position vector And for acceleration derivative of velocity vector

Q: Q1: A wheel accelerates uniformly from rest to 2000 r.p.m. in 20 seconds. What is its angular…

A: Since you have posted multiple questions but according to guidelines, we will solve the first…

Q: (2) A particle moves along the 1-aris such that the velocity is given by v(t) = 20e' +t for t > 0.…

A: Here, the velocity vector is: v(t)=20et+t7

Q: The position of the particle at time t is given by s(t) = t² – 8t + 15. %3D The particle is moving…

A: Concept used particle will move fromleft to right when velocitydvdtbecome positive.dsdt>0

Q: along the x-axis so that at time t 2 0, the acceleration of the particle is a(t) = 15Vr. ticle is 10…

A: In this question we will use basic concepts of calculus i.e concept of integration. We will use the…

Q: 20. The curve 2x2y+ y 8x +1 passes through (4, 1). Using the tangent line to the curve at the point…

A:

Q: Given the acceleration of a particle is a(t) = . If the initial velocity is v(0) =, and the initial…

A:

Q: find an equation of the tangent plane at the given point. G(u,w) = sin(uw), ( π/6 , 1)

A: Given that: G(u,w)=sin(uw) Now, Find the partial derivatives of Gu(u,w)  and  Gw(u,w) at point π6,1.…

Q: Find the direction in which the function g(x, y) = cos(xy) decreases fastest at the point (1, pi)

A:

Q: At time t 2 0, the velocity of a body moving along the s-axis is v=t2-7t+6. When is the body moving…

A:

Q: Find the displacement of an object on the interval 0 ≤ t ≤ 6 if its velocity is v (t) = 4t -√√t

A:

Q: The x- coordinate of the point on the graph of y = Vx-1 at which the tangent line is perpendicular…

A: slope of tangent of the curve y=x-1 is dydx=12x-1 slope at (x1, y1)dydx=12x1-1=m1if (x1, y1) is the…

Q: Find the equation of the tangent plane to z = ey + x + x² + 7 at the point (5, 0, 38). = Z |

A: To find the equation of tangent plane to z=ey+x+x2+7  at the point 5,0,38In general the equation of…

Q: An object with a mass of 10.00kg is launched from the ground with an initial upward velocity of…

A: Given that, An object with a mass of 10.00kg is launched from the ground with an initial upward…

Q: If the velocity is given by : (-t^2 i + 2t^2 j+ t^2 k) then the normal component of the acceleration…

A:

Q: The velocity of an object in meters per second is given by v(t) 25-, 0sts5. Find: %3D a) The…

A:

Q: Find the equation of the tangent plane to z = e9 +x + x³ + 6 at the point (3, 0, 253).

A:

Q: 3. The position of a particle travelling along a horizontal line in t seconds is s(t) = 2t° – 15t –…

A: Velocity and acceleration from displacement function of time t

Q: A cruise ship sails due south at 5.00 m/s while a coast guard patrol boat heads 29.0° north of west…

A:

Q: Q-1-At time t, the position of a body moving along the s - axis is t4 9. S = - 2t3 2t3 +t2 + 5t -- 4…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 7. Find the length of the curve f(1) = In(sin r), 0 < r < a/6.

A: Topic = Application of integration

Q: Find the equation of the tangent plane to z = e + x + x² + 4 at the point (3, 0, 17).

A:

Q: The exact value of the slope of the tangent line to the graph of the curve r = 7 + 8 cos(0), at e =…

A:

Q: For the acceleration ā = and the given initial velocity vo = and the initial position To = find the…

A:

Q: The position of a body moving along s-axis at any time 't is given by s(t) = 16t - 12t, then the…

A: The position of a body s(t)=16t3-12t

Q: If the position of a moving particle at any time 't' is defined by s(t) = 4t3 - 12t, 0 <t<6. The…

A: Given: st=4t3-12t, 0≤t≤6 We know that velocityvt and accelerationat function for given position…