the height 'h' meters above the ground of a ball 't' seconds after it has been thrown up in the air is given by the expression: h=1.5 + 3t - 2t^2
1)from what height is the ball thrown?
2) at what time does the ball hit the ground?
3) what is the greatest height that the ball reaches?
2007-09-10 10:02:16 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
1)
From 1.5 m
2)
Hits ground when h = 0
2t² - 3t - 1.5 = 0
4t² - 6t - 3 = 0
t = [6 ± √(36 + 48) ] / 8
t = [ 6 ± √(84) ] / 8
t = [6 ± 2√(21)] / 8
t = 3/4 ± (1/4)√(21) sec
t = 1.9 sec (taking + ve value for t)
3)
h `(t) = 3 - 4t = 0 for max h
t = 3/4 secs
h(3/4) = 1.5 + 9/4 - 18/16
h(3/4) = 1.5 + 18/16
h(3/4) = 42 / 16
h(3/4) = 21 / 8
Greatest height = 21 / 8 m
2007-09-17 19:34:33 · answer #1 · answered by Como 7 · 0⤊ 0⤋
a) h when t=0 is the starting point.
h=1.5+3(0)-2(0)^2
h= 1.5
b) t when h=0 is when the ball hits the ground
0=1.5=3t-2t^2 and solve for t as a quadratic equation.
Giving t=
c) differentiate dh/dt
dh/dt=3-4t
Max occurs when dh/dt=0
0=3-4t
Giving t=
You can solve the equations!
2007-09-10 19:15:40 · answer #2 · answered by Arthur C 2 · 0⤊ 0⤋
I'm not going to give you the solutions, but:-
1. Set t=0.
2. Let h=0 which will produce a quadratic equation. You will have to use the quadratic formula or complete the square. I assume you know this, if you don't, go back to your GCSE Higher textbook.
3. Do your calculus : dh/dt. Then calculate dh/dt=0.
I hope this helps. Here are the answers but it will be beneficial for you to do the working out yourself.
Answers:-
1. h=1.5
2. t=(3+sqrt(3))/4 (in surd form)
3. t=4/3=1.33333333333333333333333333333333333........
2007-09-11 08:47:57 · answer #3 · answered by mr_maths_man 3 · 0⤊ 0⤋
1. 1.5 meters
2. 1 second after it's thrown up in the air
3. 4.875 meters max height
2007-09-15 23:04:37 · answer #4 · answered by Will 4 · 0⤊ 0⤋
h=-2 t^2+3 t+1.5
2007-09-11 12:13:42 · answer #5 · answered by emc.squared 1 · 0⤊ 0⤋
1.5 meters
0=1.5+3t-2t^2
2t^2 -3t -1.5 = 0
t= (-2 +/- sqrt(9+12))/4
t=(-2 + 4.582)/4 = .645 seconds
3-4t=0
4t=3
t=.75 seconds
h=1.5 +3(.75)-2(.75)(.75)
h=1.5+2.25+1.125
h=4.875 meters
2007-09-10 17:15:11 · answer #6 · answered by bignose68 4 · 0⤊ 0⤋
1) the answer is the constant in the equation, i.e. the amount with no x value
2) set the equation equal to zero and find the non-negative answer for t
3) graph the parabola and find the highest point.
2007-09-10 17:08:07 · answer #7 · answered by soelo 5 · 0⤊ 0⤋