Santa Claus decides that landing on rooftops is too dangerous for his reindeer a

Question

Santa Claus decides that landing on rooftops is too dangerous for his reindeer and so he builds a seat which can launch him from the sleigh, directly into the chimney. The launcher can launch with a velocity of 15.0 m/s at an angle of 52.0 degrees above the horizontal. The height difference between the seat and the chimney is h=6.00 m. a. What is the maximum height, relative to the seat, that Santa will reach? [7.10m] b. What is his time of flight to the chimney? [1.68s] c. How far is the chimney away? [15.5m] d. One day as they are travelling at 80.0 km/h across an open field, Santa accidentally triggers the seat and is launched airborne. He measures his time of flight to be 2.50 s. How far does he travel horizontally? Comment

Explanation / Answer

here,

height distance , h = 6 m

velocity , u = 15 m/s

theta = 52 degree

a)

let the maximum height be hm

hm = (u * sin(theta))^2 /2g

hm = ( 15 * sin(52))^2 /2g

hm = 7.13 m

the maximum height is 7.13 m

b)

let the time of flight be t

h = ( u * sin(theta)) * t - 0.5 * g * t^2

6 = ( 15 * sin(52)) * t - 0.5 * 9.8 * t^2

t = 1.68 s

c)

distance of chimney , d = u * cos(theta) * t

d = 15 * cos(52) * 1.68

d = 15.5 m

(d)

initial horizontal speed , u0x = 80 km/h

u0x = 22.2 m/s

time of flight , t = 2.5 s

horizontal distance covered , x = ( u0x + u * cos(theta)) * t

x = ( 22.2 + 15 * cos(52)) * 2.5

x = 78.6 m

the horizontal distance covered is 78.6 m

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