A grasshopper leaps into the air from the edge of a cliff at a 47 degree angle. He reaches a maximum height 6.49 cm above the top of the cliff and travels a total horizontal distance of 1.02 m. How tall is the cliff and what is the initial speed of the grasshopper?
I've been at this and have not managed to figure it out exactly. I keep getting apparently wrong answers.
2 answers
I tried looking at formulas and other similar questions answered with different values. When I try the same formulas with these numbers I get the wrong answer so I think I am doing it wrong. The final answer I got for the height of the cliff was 4.61m.
find the vertical launch velocity (v) ... m g h = 1/2 m v^2 ... v^2 = 2 g h
... v = √(2 * 9.81 * .0649) ... m/s
launch velocity (V) = v / sin(47º)
use the launch angle to find the horizontal velocity (h)
... h = V cos(47º)
use the total horizontal distance and the horizontal velocity
... to find the flight time
find the time to maximum height
flight time minus time to max height
... is the time to fall to the bottom of the cliff
fall height minus 6.49 cm is the cliff height
be aware of the units and significant figures
... v = √(2 * 9.81 * .0649) ... m/s
launch velocity (V) = v / sin(47º)
use the launch angle to find the horizontal velocity (h)
... h = V cos(47º)
use the total horizontal distance and the horizontal velocity
... to find the flight time
find the time to maximum height
flight time minus time to max height
... is the time to fall to the bottom of the cliff
fall height minus 6.49 cm is the cliff height
be aware of the units and significant figures
1 answer