Question

Jules kicks a soccer ball off the ground and into the air with an initial velocity of 25 feet per second. Assume the starting height of the ball is 0 feet. Approximately what maximum height does the soccer ball reach?

0.8 ft

1.6 ft

9.8 ft

19.6 ft

Approximately, how long does it take until the soccer ball hits the ground again?

0.6 sec

0.8 sec

1.6 secs

2.8 secs

Answer 1

Assuming that Jules kicks the ball completely vertically, then you can use one of the famous kinematics equations (I'll spare you the derivation here): (v-final)^2 - (v-initial)^2 = 2*a*height In your case, the ball's final velocity (at its maximum height) is zero! Your acceleration is -g = -32 feet per second per second, and your initial velocity is 25 feet per second. So you have: height = - (25)^2 / (2*-32) = 625 / 64 = 9.8 feet

Answer 2

at maximum height velocity v =
u = initial velocity = 25, s = height, a = -32 ft/s/s
v^2 =u ^2 + 2 as
0 = 25^2 + 2 * -32 * s
0 = 625 - 16s
16s = 625

Answer 3

aawwww - i mucked that up

its 0 = 25^2 - 64s
s = 625/64

Answer 4

yes its 9.8 ft

Answer 5

So he was right. The answer to the first one is 9.8ft. But what about the second question?

Answer 6

use another constant acceleration equation

s = displacement = 0, u = 25, a = -32, t = ?

s = ut + 0.5at^2
0 = 25t - 16t^2
16t^2 - 25t = 0
t(16t - 25) = 0

can you solve this megan?

Answer 7

Is it 1.6?

Answer 8

yes!!
good one

Answer 9

t = 25/16 = 1.6 to 1 D P

Answer 10

Can you help me with two more of these problems? i would really appreciate it!

Answer 11

ok

Answer 12

Amir pitched a baseball at an initial height of 5.9 feet with a velocity of 73.16 feet per second. About how long will it take the ball Amir pitched to hit the ground?

4.66 secs

2.94 secs

2.35 secs

1.47 secs

Answer 13

S = Vit + ½at²
5.9 = 73.16t + ½(32.2)t²
16.2t² + 73.16 t - 5.9 = 0
t = [-(73.16) ±√73.16² - 4(16.1)(-5.9)]/2(16.1)
t = -73.16 ± 75.71 / 32.2
t = 0.079 sec & 4.6 sec

Answer 14

wow - thats fast!!

Answer 15

Thanks!

Answer 16

Ken is building a table. He attached planks of wood and now wants to build a border around the planks. The area of the entire table should be no larger than 3,276 square inches. All together, the planks are 36 inches wide and 72 inches long. Which quadratic equation represents the area of the planks and border combined? (The border must have equal width on each side.)

4x2 + 216x + 2,592 = 0

4x2 + 216x − 684 = 0

2x2 + 216x − 3,276 = 0

x2 + 108x + 3,276 = 0

Answer 17

i'm looking at deal or no deal - exciting bit - so if lawrence hasn't done it in record time i'll have a go

Answer 18

I'm kind of in a rush....could you please help me

Answer 19

@lawrenceh123 please help

Answer 20

om - im a bit confused wit with this one
the area of one plank = 36 * 72 = 2592

Answer 21

so i guess the first one would be the answer

Answer 22

4x2 + 216x + 2,592 = 0?

Answer 23

If he makes the border x inches wide, then there will be an area of
36*x of border at each end and an area of
72*x of border on each longer side. At each of the 4 corners, there will be an additional
x*x border area. So the entire area of a maximum-size tabletop is
4*x*x + 2*36x + 2*72x + 36*72 = 3,276 square inches. Simplifying this, we get
4x^2 + 216x + 2,592 = 3,276
4x^2 + 216x − 684 = 0
which is the second proposed answer.

Answer 24

ahhh - yes - good work lawrence

Answer 25

ty

Answer 26

ty