A particle initially located at the origin has an acceleration of a \" 1.00j m/s

Question

A particle initially located at the origin has an acceleration of a " 1.00j m/s2 and an initial velocity of 9.001 m/s. (a) Find the vector position of the particle at any time t (where t is measured in seconds). 901 05 (b) Find the velocity of the particle at any time t (c) Find the coordinates of the particle at t-6.00 25)m x 54.0 (d) Find the speed of the particle at t-6.00s 10.82 is fired in such a way that its 4 P016.W A ball is tossed from an upper-story window of a building. The ball is given an initial velocity of 8.20 m/s at an angle of 24.0° below the horizontal. 1It strikes the (a) How far horizontally from the base of the building does the ball strike the ground? 45 (b) Find the height from which the ball was thrown. 196.411 m

Explanation / Answer

(a)
d(t) = 9 t i + 0.5 t^2 j

(b)
v(t) = 9 i + 1t j

(c)
x = 54 m
y = 18 m

(d)
v(t) = 9 i + 6 j
v = (9^2 + 6^2)^(1/2) = 10.82

Question 5)
Let maximum height be h
The range = 3.5h

At maximum height the velocity is 0

v^2 = u^2 + 2as
0 = uy^2 + 2(-9.8)h
uy = (2*9.8*h)^(1/2)
h = (usin(theta))^2/2g

R = (usin(2theta))^2/g
3h = (usin(2theta))^2/g

1/3 = (sin(theta))^2/(2(sin(2theta))^2)
1/3 = (sec^2(theta))/8
(8/3)^(1/2) = sec(theta)
theta = arcsec((8/3)^(1/2))
theta = 52.24 degrees

Please upvote if the answers are correct.

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