Children are playing with a remote-controlled toy jeep in an open horizontal fie

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Children are playing with a remote-controlled toy jeep in an open horizontal field. at some ... Your question has been answered Let us know if you got a helpful answer. Rate this answer Question: Children are playing with a remote-controlled toy jeep in an open horizontal field. At some time,... Children are playing with a remote-controlled toy jeep in an open horizontal field. At some time, the jeep is located (relative to a rock which they are using as the origin) at r0 = (12.5î 9.00) m and has a velocity of v0 = (7.00î + 3.00) m/s. If, for a time interval t =10.0 s, the jeep experiences a constant acceleration a and acquires a new velocity v = (3.00î 19.00) m/s, determine the following for the jeep. (Express your answer in vector form.)

(a) position vector at time t = 10.0 sec

r(t = 10.0 s) =

(b) velocity vector time t = 5.00 sec

v(t = 5.00 s) =

Explanation / Answer

initial position is ro = 12.5i - 9j

initial velocity is Vo = 7i + 3j

for dt = 10 sec
v = 3 i - 19 j

then accelaration is a = (3-7)i +(-19-3) j / 10 = (-4/10)i -(22/10)j = -0.4 i -2.2 j

ax = -0.4 m/s^2

ay = -2.2 m/s^2

a) using kinematic equations

dispalcement along x-axis is

x = xo + (Vox*t)+(0.5*ax*t^2)

x = 12.5 + (7*10)-(0.5*0.4*10^2) = 62.5 m

y = (yo)+(voy*t)+(0.5*ay*t^2)

y = -9 + (3*10)-(0.5*2.2*10^2) = -89 m

then position vector is r = (62.50 i -89.0 j) m

b) after t = 5 sec

vx = vox +(ax*t) = 7-(0.4*5) = 5 m/sec

vy = voy+(ay*t) = 3-(2.2*5) = -8 m/sec

velocity vector is v= (5.0 i -8.0 j) m/s

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