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A projectile is launched from ground level with an initial speed of 47 m/s at an angle of 0.6 radians above the horizontal. It s

Zarrin [17]

Answer:

30.67m

Explanation:

Using one of the equations of motion as follows, we can describe the path of the projectile in its horizontal or vertical displacement;

s = ut ± $\frac{1}{2} at^2$ ------------(i)

Where;

s = horizontal/vertical displacement

u = initial horizontal/vertical component of the velocity

a = acceleration of the projectile

t = time taken for the projectile to reach a certain horizontal or vertical position.

Since the question requires that we find the vertical distance from where the projectile was launched to where it hit the target, equation (i) can be made more specific as follows;

h = vt ± $\frac{1}{2} at^2$ ------------(ii)

Where;

h = vertical displacement

v = initial vertical component of the velocity = usinθ

a = acceleration due to gravity (since vertical motion is considered)

t = time taken for the projectile to hit the target

<em>From the question;</em>

u = 47m/s, θ = 0.6rads

=> usinθ = 47 sin 0.6

=> usinθ = 47 x 0.5646 = 26.54m/s

t = 1.7s

Take a = -g = -10.0m/s (since motion is upwards against gravity)

Substitute these values into equation (ii) as follows;

h = vt - $\frac{1}{2} at^2$

h = 26.54(1.7) - $\frac{1}{2} (10)(1.7)^2$

h = 45.118 - 14.45

h = 30.67m

Therefore, the vertical distance is 30.67m

7 0

4 years ago

Two fans are watching a baseball game from different positions. One fan is located directly behind home plate, 18.3 mfrom the ba

hjlf

Answer:

Δt = 0.315s

Explanation:

To calculate the time difference, in which both fans hear the batterstrike, you first calculate the time which takes the sound to travel the distances to both fans:

$t_1=\frac{d_1}{v_s}$

$t_2=\frac{d_2}{v_s}$

d1: distance to the first fan = 18.3 m

d2: distance to the second fan = 127 m

vs: speed of sound = 345 m/s

You replace the values of the parameters to calculate t1 and t2:

$t_1=\frac{18.3m}{345m/s}=0.053s\\\\t_2=\frac{127m}{345m/s}=0.368s$

The difference in time will be:

$\Delta t =t_2-t_2=0.368s-0.053s=0.315s$

Hence, the time difference between hearing the sound at the location s of both fans is 0.315s

4 0

3 years ago

A 2-kW electric heater takes 15 min to boil a quantity of water. If this is done once a day and power costs 10 cents per kWh, wh

frozen [14]

Answer:

Explanation:

Given data

power P= 2 kW

time t= 15 min to hours = 15/60= 1/4 h

cost of power consumption per kWh= 10 cent = $0.1

We are expected to compute the cost of operating the heater for 30 days

but let us computer the energy consumption for one day

Energy of heater for one day= 2* 1/4 = 0.5 kWh

the cost of operating the heater for 30 days= 0.5*0.1*30= $1.50

<u><em>Hence it will cost $1.50 for 30 days operation</em></u>

4 0

3 years ago

A conductor bent into a semicircle of total length 3.88 m is placed in a 2.0 T magnetic field perpendicular to the plane of the

ivolga24 [154]

Answer:

Magnetic force, F = 38.95 N

Explanation:

Given that,

Length of the conductor, L = 3.88 m

Magnetic field, B = 2 T

Current flowing in the conductor, I = 5.02 A

The magnetic field perpendicular to the plane of the semicircle. The angle between the magnetic field and the plane is 90 degrees. The expression for the magnetic force is given by:

$F=ILB\ sin\theta$