If the acceleration is constant, the following equations apply: Here a_x, v_x, x

Question

If the acceleration is constant, the following equations apply: Here a_x, v_x, x_a, a_y, v_ay, y_a are all constants. F^vector = (1/2 a_x t^2 + v_ax t + x_a)i^^+ (1/2 a_y t^2 + v_ay t + y_a)j^^(or, x(t) = 1/2 a_x t^2 + v_ax t + x_a and y(t) = 1/2 a_y t^2 + v_ay t + y_a) v^vector = (a_x t + v_ax)i^+ (a_y t + v_ay)j^^(or: v_x(t) = a_x (t) + v_ax and v_y (t) = a_y (t) + v_ay) a^vector = a_x i^^+ a_y j^^For all the following problems, define x_0 = 0. Assume free fall. Define +j as upwards, and +ii to the right. Put answers on a separate sheet. I throw a ball straight up, mass m = 5kg, at an initial spedd of 3 m/s, at an initial height of 1.7m. a) V_ox = b) V_oy = c) a_x = d) a_y = e) y_0 = f) Write the full function for F^vecor, using the answers to questions a-e, and using i-j notation. g) Write the full function for v^vector, using the answers to questions a-e, and using i-j notation. h) Obtain the position r^vector at t = 0.5 seconds. i) Obtain the velocity v^vector at t = 0.5 seconds. I throw a ball, mass m=5kg, at an initial speed of 3m/s, at an initial height of 1.7m, but at an angle of 30 degree respect to the horizontal. a) V_ox = b) V_oy = c) a_x = d) a_y = e) y_o = f) Write the full function for r^vecor, using the answers to questions a-e, and using i-j notation. g) Write the full function for v^vector, using the answers to questions a-e, and using i-j notation. h) Obtain the position r^vector at t = 0.5 seconds. i) Obtain the velocity v^vector at t = 0.5 seconds.

Explanation / Answer

a)

v0x = 0

b)

voy = 3 m/s

(c)

ax = 0

(d)

ay = -g = -9.8 m/s^2

(e)

y0 = 1.7 m

(f)

r = 0i - (1/2*9.8*t^2 + 3t + 1.7 )j

(g)

v = 0i + (-9.8*t + 3)j

(h)

r = 0i (-1/2*9.8*0.5^2 + 3*0.5 + 1.7)j = 1.975 j

(i)

v = 0i + (-9.8*0.5 + 3 ) j = -1.9 j

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#problem 2

a)

v0x = v0*costheta = 3*cos30 = 2.598 m/s

b)

voy = v0*sin30 = 1.5 m/s

(c)

ax = 0

(d)

ay = -g = -9.8 m/s^2

(e)

y0 = 1.7

(f)

r = ( 2.598*t )i + (-1/2*9.8*t^2 + 1.5t + 1.7 )j

(g)

v = 2.598i + (-9.8*t + 1.5)j

(h)

r = 2.598*0.5i + (-1/2*9.8*0.5^2 + 1.5*0.5 + 1.7)j = 2.598i + 1.225j

(i)

v = 2.598 i + (-9.8*0.5 + 1.5 ) j = 2.598 i - 3.4j

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