Quadratic Story Problems Day I
The formual h = -16t2 – vot + s (for feet) or h = -4.9t2 – vot + s (for meters) can be used when things are rising or falling on the earth. Note that:
h: the ending height (in feet or meters)
t: time in seconds
vo: original velocity (in ft/sec or m/sec)
s: starting height (in feet or meters)
1) You launch a model rocket from the ground with an initial velocity of 95 ft/sec.
A) When will it hit the ground? B) How high will the ball go? C) After how many seconds will the rocket have an altitude of 114 feet?
2) You throw a baseball in the air with an initial velocity of 28 ft/sec. The baseball is 5 ft high when it leaves your hand.
A) After how many seconds will it hit the ground? B) How high will the ball go? C) When will the ball be 15 ft high?
3) During a chemistry experiment, the cork in a 6”tall beaker with ad effervescent solution pops off with an initial velocity of 20 ft/sec.
A) How many seconds does it take for the cork to hit the table? B) How high will the cork go? C) When will the cork be 9” high?
4) A diver steps off a 12-ft high diving board with an initial velocity of 0 ft/sec.
How many seconds later does he hit the water?
5) A person springs off a 12 foot diving board with an initial velocity of 15 ft/sec.
A) How many seconds does it take for her to hit the water?
6) You drop a softball glove out of your bedroom window that is 28 feet off the ground.
A) How long will it take to hit the ground?
7) How long will it take for a walnut to hit the ground if it falls from a branch that is 55 feet off the ground?
8) While standing on a ladder that is 10 feet above the ground, you ask a friend to toss you a paint brush. The starting height of the paint brush is 5 feet. The starting velocity is 20 ft/sec. Did the friend
toss the paint brush high enough to reach you? If you do not catch the paint brush, how high will the paint brush go?
KEY
1) A: 5 secs B: it will hit a max ht of about 141 ft in approximately 2.969 secs C: at 1.64 secs and again at 4.29 secs
2) A: in 1.91 secs B: in 7/8 of a sec, it will reach a max ht of 17’3” C: it will reach 15 ft in ½ secs and at 1¼ secs
3) A: in 1.27 secs B: in 5/8 secs it will reach a ht of 6’ 9” C: at about 0.013 secs and again at 1.24 secs
4) in 1.155 secs
5) in 1.45 secs
6) in approximately 1.32 secs
7) in approximately 1.85 secs