Question

Mighty Casey hits two baseballs out of the park. The path of the first baseball can be described by the displacement (distance and direction) vector,

b1 = 100 i ^ + 10 j ^. The path of the second baseball can be described by the displacement vector b2 = 90 i ^ + (−20) j ^.

(a) How much farther did the first ball travel than the second? (Round your final answer to the nearest tenth.)

(b) How far are the baseballs apart? (Round your final answer to the nearest tenth.)

Answer 1

a) 8.3 units of length

b) 31.6 units of length

Explanation:

a) The distances traveled by each ball are given by:

`d_1^2=100^2+10^2=10,100\\d_1=100.5\\\\d_2^2=90^2+(-20^2)=8,500\\d_2=92.2`

The diference between the distance traveled by both balls is:

`d_1-d-2=100.5-92.2\\d_1-d_2=8.3`

The first ball traveled 8.3 units of length farther than the second ball.

b) The distance between both balls is:

`d^2=(i_1-i_2)^2+(j_1-j_2)^2\\d^2=(100-90)^2+(10-(-20))^2\\d^2=1,000\\d=31.6`

The balls are 31.6 units of length apart.