A grasshopper leaps into the air from the edge of a vertical cliff, as shown in Fig. P3.57. Find (a) the initial speed of the grasshopper and (b) the height of the cliff.

Solution 63P

Step 1 of 5:

(a) the initial speed of the grasshopper

Let us consider vertical component of velocity,

where,as it reaches max height, its final velocity will be zero,

Initial velocity =v sin 50,

distance s= 6.74 cm = 0.0674 m

Acceleration , a=g=

Substituting given data in above equation,

v = 1.5 m/s

Therefore, the initial velocity of the grasshopper is 1.5 m/s.

Step 2 of 5:

(b) the height of the cliff.

Using fundamental relation of speed,

For horizontal component,

Time of flight, t=

Substituting distance(horizontal)= 1.06 m and speed(horizontal component), v= v cos 50

t=

Using v = 1.5 m/s

t=

t = 1.099 s

Step 3 of 5:

Time taken to reach maximum height(vertical component),

Using v = 1.5 m/s

0.1175 s