Unit 5 Lesson 1 Solutions
6
Activity 2
A dragster races down a 400 m strip in 8 s. Its distance (m) from the starting line after t seconds is s(t) = 6t
2
+ 2t
.
a) Find the dragster’s acceleration and velocity as it crosses the finish line.
b) How fast was it moving 60 m down the strip?
v(t) = 12t + 2
a(t) = 12
crosses finish line at 8 seconds
v(8) = 12(8) + 2 = 98 m/s
a(8) = 12 m/s
2
60 = 6t
2
+ 2t
0 = 6t
2
+ 2t - 60
0 = 3t
2
+ t - 30
0 = (3t + 10)(t - 3)
t = -
10
3
inadmissible
t = 3
v(3) = 12(3) + 2 = 38 m/s
Activity 3
A major-league baseball pitcher can throw a ball with an initial vertical velocity of 35 m/s. Assuming that acceleration due to gravity is -9.8 m/s
2
and the ball is released at 2 m then s(t) = 2 + 35t - 4.9t
2
. Could the pitcher hit the ceiling of the SkyDome which is 86 m above the ground?
Reaches max height when velocity is zero
v(t) = 35- 9.8t
0 = 35 - 9.8t
t = 35
9.8
t = 3.57
s(3.57) = 2 + 35(3.57) - 4.9(3.57)
2
= 64.5
therefore maximum height of the ball is 64.5m so it cannot hit the ceiling of the SkyDome which is 86 m
alternately can solve for when s(t) = 86
86 = 2 + 35t - 4.9t
2
-4.9t
2
+ 35t - 84 = 0
b
2
- 4ac = 35
2
- 4(-4.9)(-84)
b
2
- 4ac = -421.4
discriminant < 0 so no roots
