Agrasshopper jumps a horizontal distance of 1.50 m from rest, with an initial velocity at a 43.0° angle with respect to the horizontal.
(a) find the initial speed of the grasshopper.
m/s
(b) find the maximum height reached.
m

(a)v₀ =3.84 m/s

(b) h= 0.35 m

Explanation:

The grasshopper describes a parabolic path.

The parabolic movement results from the composition of a uniform rectilinear motion (horizontal ) and a uniformly accelerated rectilinear motion of upward or downward motion (vertical ).

The equation of uniform rectilinear motion (horizontal ) for the x axis is :

x = xi + vx*t   Equation (1)

Where:  

x: horizontal position in meters (m)

xi: initial horizontal position in meters (m)

t : time (s)

vx: horizontal velocity  in m/s  

The equations of uniformly accelerated rectilinear motion of upward (vertical ) for the y axis  are:

y= y₀+(v₀y)*t - (1/2)*g*t² Equation (2)

Where:  

y: vertical position in meters (m)  

y₀ : initial vertical position in meters (m)  

t : time in seconds (s)

v₀y: initial  vertical velocity  in m/s  

g: acceleration due to gravity in m/s²

Data

g = 9.8 m/s²

v₀ , at an angle  α=43.0°  above the horizontal

xi=0

x=  1.50 m

y₀=0

x-y components of v₀

v₀x =  v₀cos43.0° = vx

v₀y =  v₀sin43.0°

Calculation of the time it takes for the grasshopperl to toch the ground

We replace data in the equation (1)

x = 0 + vx*t  =  (v₀cos43.0°)*t

t= x/(v₀cos43.0°)

t= 1,5/(v₀cos43.0°) Equation (3)

We replace t= 1,5/(v₀cos43°),y₀=0, y = 0,:when the grasshopper touches the ground  in the equation (2)

y=(v₀y)*t - (1/2)*g*t²

0=(v₀sin43°)*(1,5/(v₀cos43°) - (1/2)*(9.8)*1,5²/(v₀cos43°)²

0= 1,5*tan43° - 11.025/(v₀cos43°)²

11.025/(v₀cos43°)² = 1,5*tan43°

11.025 = (1,5*tan43°)*(v₀cos43°)²

(v₀cos43°)² = (11.025 )/ 1,5*(tan43°)

v₀² = (11.025 )/ (1,5*tan43°)(cos43°)²

v₀² = 14.73

v₀ = 3.84 m/s

Flight time

in the Equation (3):

t = 1,5/(v₀cos43.0°) = 1,5/(3.84*cos43°)

t = 0.534 s

(b) Maximum height reached (h)

The time to reach maximum height (h) is half the time of flight time :

th=0.534 s /2 = 0.267 s

We apply the  Equation (2)  

y= (v₀y)*t - (1/2)*g*t²

h= ( 3.84*sin 43°)*( 0.267) - (1/2)*(9.8)*( 0.267)²

h= 0.35 m

explanation:

earth's surface is mainly heated by the absorption of infrared radiation from the sun.

evaporation occurs because molecules in liquid water are warmed ( usually by the sun) and vibrate quicker, becoming less dense and rise.

condensation occurs because molecules in water vapor are cooled and therefore vibrate more slowly thus becoming more dense and eventually fall to earth.

lines of equal barometric pressure on a weather map are called: isobars : lines of equal temp on a weather map are called: isotherms.​

answer: electrons