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{
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{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 19: Relative Motion"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 19.1: Relative_Velocity.sce"
]
},
{
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"execution_count": null,
"metadata": {
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"source": [
"// Initilization of variables\n",
"v_t=10 // m/s // velocity of the train\n",
"v_s=5 // m/s // velocity of the stone\n",
"// Calculations\n",
"// Let v_r be the relative velocity, which is given as, (from triangle law)\n",
"v_r=sqrt(v_t^2+v_s^2) // m/s\n",
"// The direction ofthe stone is,\n",
"theta=atand(v_s/v_t) // degree\n",
"// Results\n",
"clc\n",
"printf('The velocity at which the stone appears to hit the person travelling in the train is %f m/s \n',v_r)\n",
"printf('The direction of the stone is %f degree \n',theta)"
]
}
,
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 19.2: Relative_Velocity.sce"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"// Initilization of variables\n",
"v_A=5 // m/s // speed of ship A\n",
"v_B=2.5 // m/s // speed of ship B\n",
"theta=135 // degree // angle between the two ships\n",
"// Calculations\n",
"// Here,\n",
"OA=v_A // m/s\n",
"OB=v_B // m/s\n",
"// The magnitude of relative velocity is given by cosine law as,\n",
"AB=sqrt((OA^2)+(OB^2)-(2*OA*OB*cosd(theta))) // m/s\n",
"// where AB gives the relative velocity of ship B with respect to ship A\n",
"// Applying sine law to find the direction, Let alpha be the direction of the reative velocity, then\n",
"alpha=asind((OB*sind(theta))/(AB)) // degree\n",
"// Results\n",
"clc\n",
"printf('The magnitude of relative velocity of ship B with respect to ship A is %f m/s \n',AB)\n",
"printf('The direction of the relative velocity is %f degree \n',alpha)"
]
}
,
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 19.3: Relative_Velocity.sce"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"// Initilization of variables\n",
"v_c=20 // km/hr // speed at which the cyclist is riding to west\n",
"theta_1=45 // degree // angle made by rain with the cyclist when he rides at 20 km/hr\n",
"V_c=12 // km/hr // changed speed\n",
"theta_2=30 // degree // changed angle when the cyclist rides at 12 km/hr\n",
"// Calculations\n",
"// Solving eq'ns 1 & 2 simultaneously to get the values of components(v_R_x & v_R_y) of absolute velocity v_R. We use matrix to solve eqn's 1 & 2.\n",
"A=[1 1;1 0.577]\n",
"B=[20;12]\n",
"C=inv(A)*B // km/hr\n",
"// The X component of relative velocity (v_R_x) is C(1)\n",
"// The Y component of relative velocity (v_R_y) is C(2)\n",
"// Calculations\n",
"// Relative velocity (v_R) is given as,\n",
"v_R=sqrt((C(1))^2+(C(2))^2) // km/hr\n",
"// And the direction of absolute velocity of rain is theta, is given as\n",
"theta=atand(C(2)/C(1)) // degree\n",
"// Results \n",
"clc\n",
"printf('The magnitude of absolute velocity is %f km/hr \n',v_R)\n",
"printf('The direction of absolute velocity is %f degree \n',theta)"
]
}
,
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 19.4: Relative_Velocity.sce"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"// Initiization of variables\n",
"a=1 // m/s^2 // acceleration of car A\n",
"u_B=36*(1000/3600) // m/s // velocity of car B\n",
"u=0 // m/s // initial velocity of car A\n",
"d=32.5 // m // position of car A from north of crossing\n",
"t=5 // seconds\n",
"// Calculations\n",
"// CAR A: Absolute motion using eq'n v=u+at we have,\n",
"v=u+(a*t) // m/s\n",
"// Now distance travelled by car A after 5 seconds is given by, s_A=u*t+(1/2)*a*t^2\n",
"s_A=(u*t)+((1/2)*a*t^2)\n",
"// Now, let the position of car A after 5 seconds be y_A\n",
"y_A=d-s_A // m // \n",
"// CAR B:\n",
"// let a_B be the acceleration of car B\n",
"a_B=0 // m/s\n",
"// Now position of car B is s_B\n",
"s_B=(u_B*t)+((1/2)*a_B*t^2) // m\n",
"x_B=s_B // m\n",
"// Let the Relative position of car A with respect to car B be BA & its direction be theta, then from fig. 19.9(b)\n",
"OA=y_A\n",
"OB=x_B\n",
"BA=sqrt(OA^2+OB^2) // m\n",
"theta=atand(OA/OB) // degree\n",
"// Let the relative velocity of car A w.r.t. the car B be v_AB & the angle be phi. Then from fig 19.9(c). Consider small alphabets\n",
"oa=v\n",
"ob=u_B\n",
"v_AB=sqrt(oa^2+ob^2) // m/s\n",
"phi=atand(oa/ob) // degree\n",
"// Let the relative acceleration of car A w.r.t. car B be a_A/B.Then,\n",
"a_AB=a-a_B // m/s^2\n",
"// Results\n",
"clc\n",
"printf('The relative position of car A relative to car B is %f m \n',BA)\n",
"printf('The direction of car A w.r.t car B is %f degree \n',theta)\n",
"printf('The velocity of car A relative to car B is %f m/s \n',v_AB)\n",
"printf('The direction of car A w.r.t (for relative velocity)is %f degree \n',phi)\n",
"printf('The acceleration of car A relative to car B is %f m/s^2 \n',a_AB)"
]
}
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